A study was conducted on the effect of time delay and structural parameters on the vibration reduction of a time delayed coupled negative stiffness dynamic absorber in nonlinear vibration reduction systems. Taking dyn...A study was conducted on the effect of time delay and structural parameters on the vibration reduction of a time delayed coupled negative stiffness dynamic absorber in nonlinear vibration reduction systems. Taking dynamic absorbers with different structural and control parameters as examples, the effects of third-order nonlinear coefficients, time-delay control parameters, and negative stiffness coefficients on reducing the replication of the main system were discussed. The nonlinear dynamic absorber has a very good vibration reduction effect at the resonance point of the main system and a nearby area, and when 1 increases to a certain level, the stable region of the system continues to increase. The amplitude curve of the main system of a nonlinear dynamic absorber will generate Hop bifurcation and saddle node bifurcation in the region far from the resonance point, resulting in almost periodic motion and jumping phenomena in the system. For nonlinear dynamic absorbers with determined structural parameters, time-delay feedback control can be adopted to control the amplitude of the main system. For different negative stiffness coefficients, there exists a minimum damping point for the amplitude of the main system under the determined system structural parameters and time-delay feedback control parameters.展开更多
Electronic processes within atoms and molecules reside on the timescale of attoseconds. Recent advances in the laserbased pump-probe interrogation techniques have made possible the temporal resolution of ultrafast ele...Electronic processes within atoms and molecules reside on the timescale of attoseconds. Recent advances in the laserbased pump-probe interrogation techniques have made possible the temporal resolution of ultrafast electronic processes on the attosecond timescale, including photoionization and tunneling ionization. These interrogation techniques include the attosecond streak camera, the reconstruction of attosecond beating by interference of two-photon transitions, and the attoclock. While the former two are usually employed to study photoionization processes, the latter is typically used to investigate tunneling ionization. In this review, we briefly overview these timing techniques towards an attosecond temporal resolution of ionization processes in atoms and molecules under intense laser fields. In particular, we review the backpropagation method, which is a novel hybrid quantum-classical approach towards the full characterization of tunneling ionization dynamics. Continued advances in the interrogation techniques promise to pave the pathway towards the exploration of ever faster dynamical processes on an ever shorter timescale.展开更多
This paper is concerned with consensus of a secondorder linear time-invariant multi-agent system in the situation that there exists a communication delay among the agents in the network.A proportional-integral consens...This paper is concerned with consensus of a secondorder linear time-invariant multi-agent system in the situation that there exists a communication delay among the agents in the network.A proportional-integral consensus protocol is designed by using delayed and memorized state information.Under the proportional-integral consensus protocol,the consensus problem of the multi-agent system is transformed into the problem of asymptotic stability of the corresponding linear time-invariant time-delay system.Note that the location of the eigenvalues of the corresponding characteristic function of the linear time-invariant time-delay system not only determines the stability of the system,but also plays a critical role in the dynamic performance of the system.In this paper,based on recent results on the distribution of roots of quasi-polynomials,several necessary conditions for Hurwitz stability for a class of quasi-polynomials are first derived.Then allowable regions of consensus protocol parameters are estimated.Some necessary and sufficient conditions for determining effective protocol parameters are provided.The designed protocol can achieve consensus and improve the dynamic performance of the second-order multi-agent system.Moreover,the effects of delays on consensus of systems of harmonic oscillators/double integrators under proportional-integral consensus protocols are investigated.Furthermore,some results on proportional-integral consensus are derived for a class of high-order linear time-invariant multi-agent systems.展开更多
In this paper,we consider a 2-degrees-of-freedom(DOF)helicopter system subject to long input delays and uncertain system parameters.To address the challenges including unknown system parameters and input delays in con...In this paper,we consider a 2-degrees-of-freedom(DOF)helicopter system subject to long input delays and uncertain system parameters.To address the challenges including unknown system parameters and input delays in control design,we develop an adaptive predictor-feedback control law to achieve trajectory tracking.Stability of the closed-loop system is further established,where the tracking errors are shown to converge towards zero.Through simulation and experiments on the helicopter system,we illustrate that tracking of a desired trajectory is achieved with the proposed control scheme.展开更多
RSs(Radar Systems)identify and trace targets and are commonly employed in applications like air traffic control and remote sensing.They are necessary for monitoring precise target trajectories.Estimations of RSs are n...RSs(Radar Systems)identify and trace targets and are commonly employed in applications like air traffic control and remote sensing.They are necessary for monitoring precise target trajectories.Estimations of RSs are non-linear as the parameters TDEs(time delay Estimations)and Doppler shifts are computed on receipt of echoes where EKFs(Extended Kalman Filters)and UKFs(Unscented Kalman Filters)have not been examined for computations.RSs,certain times result in poor accuracies and SNRs(low signal to noise ratios)especially,while encountering complicated environments.This work proposes IUKFs(Iterated UKFs)to track onlinefilter performances while using optimization techniques to enhance outcomes.The use of cost functions can assist state corrections while lowering costs.A new parameter is optimized using MCEHOs(Mutation Chaotic Elephant Herding Optimizations)by linearly approximating system non-linearity where OIUKFs(Optimized Iterative UKFs)predict a target's unknown parameters.To obtain optimal solutions theoretically,OIUKFs take less iteration,resulting in shorter execution times.The proposed OIUKFs provide numerical approximations which are derivative-free implementations.Simulation evaluation results with estimators show better performances in terms of reduced NMSEs(Normalized Mean Square Errors),RMSEs(Root Mean Squared Errors),SNRs,variances,and better accuracies than current approaches.展开更多
Breast cancer in women is a complicated and multifaceted disease. Studies have demonstrated that hyperglycemia is one of the most significant risk factors for breast cancer. Hyperglycemia is when the sugar level in hu...Breast cancer in women is a complicated and multifaceted disease. Studies have demonstrated that hyperglycemia is one of the most significant risk factors for breast cancer. Hyperglycemia is when the sugar level in human blood is too high, which means excess glucose. Glucose excess can encourage the growth, invasion, and migration of breast cancer cells at the cellular level. Though, the effects of glucose on the dynamics of breast cancer cells have been examined mathematically by a system of ordinary differential equations. However, the non-instantaneous biological occurrences leading to the secretion of immuno-suppressive cytokines by tumors to evade immune surveillance and the immune cells’ derivation of cytokines to attack the tumor cells are not yet discussed. Therefore, investigating the biological process involved in the dynamics of tumors, immune and normal cells with excessive glucose concentration is inviolable to determining the best procedure for controlling tumors’ uncontrollable growth. Time delay, denoted by τ, is used to describe the time tumor cells take to secrete immunosuppressive cytokines to evade immune surveillance and the time immune cells take to recognize and attack the tumor cells. We have studied the local stability analysis of the biological steady states in both delayed and non-delayed system. The Routh-Hurwitz stability criterion is used to analyze the dynamical equilibrium of the cells’ population. Hopf bifurcation was analyzed by using time delay s as a bifurcation parameter. The analytical results suggest an unstable scenario for a tumor-free equilibrium point as normal cells are bound to grow to their carrying capacity. The result predicts a stable system for coexisting equilibrium when the interaction is instantaneous (τ = 0). However, when τ > 0, the coexisting equilibrium point switches from stable to unstable. The numerical results not only validate all the analytical results but also show the case of possible situations when glucose concentration is varied, indicating that both tumor growth and immune system efficiency are highly affected by the level of glucose in the blood. This concluded that the delay in the secretion of cytokines by immune cells and derivation cytokines by the tumors helps to identify the possible chaotic situation under different glucose concentration and the extent to which such delay can have on restoration of the normal cells when glucose concentration is low.展开更多
It is an important issue to estimate parameters of fractional-order chaotic systems in nonlinear science, which has received increasing interest in recent years. In this paper, time delay and fractional order as well ...It is an important issue to estimate parameters of fractional-order chaotic systems in nonlinear science, which has received increasing interest in recent years. In this paper, time delay and fractional order as well as system’s parameters are concerned by treating the time delay and fractional order as additional parameters. The parameter estimation is converted into a multi-dimensional optimization problem. A new scheme based on artificial bee colony(ABC) algorithm is proposed to solve the optimization problem. Numerical experiments are performed on two typical time-delay fractional-order chaotic systems to verify the effectiveness of the proposed method.展开更多
In complex environments, many distributed multiagent systems are described with the fractional-order dynamics.In this paper, containment control of fractional-order multiagent systems with multiple leader agents are s...In complex environments, many distributed multiagent systems are described with the fractional-order dynamics.In this paper, containment control of fractional-order multiagent systems with multiple leader agents are studied. Firstly,the collaborative control of fractional-order multi-agent systems(FOMAS) with multiple leaders is analyzed in a directed network without delays. Then, by using Laplace transform and frequency domain theorem, containment consensus of networked FOMAS with time delays is investigated in an undirected network, and a critical value of delays is obtained to ensure the containment consensus of FOMAS. Finally, numerical simulations are shown to verify the results.展开更多
The stabilization problem of distributed proportional-integral-derivative(PID)controllers for general first-order multi-agent systems with time delay is investigated in the paper.The closed-loop multi-input multi-outp...The stabilization problem of distributed proportional-integral-derivative(PID)controllers for general first-order multi-agent systems with time delay is investigated in the paper.The closed-loop multi-input multi-output(MIMO)framework in frequency domain is firstly introduced for the multi-agent system.Based on the matrix theory,the whole system is decoupled into several subsystems with respect to the eigenvalues of the Laplacian matrix.Considering that the eigenvalues may be complex numbers,the consensus problem of the multi-agent system is transformed into the stabilizing problem of all the subsystems with complex coefficients.For each subsystem with complex coefficients,the range of admissible proportional gains is analytically determined.Then,the stabilizing region in the space of integral gain and derivative gain for a given proportional gain value is also obtained in an analytical form.The entire stabilizing set can be determined by sweeping proportional gain in the allowable range.The proposed method is conducted for general first-order multi-agent systems under arbitrary topology including undirected and directed graph topology.Besides,the results in the paper provide the basis for the design of distributed PID controllers satisfying different performance criteria.The simulation examples are presented to check the validity of the proposed control strategy.展开更多
This work studies the stabilization of a class of control systems that use communication networks as signal transmission medium. The lateral motion of independently actuated four-wheel vehicle is modeled as an uncerta...This work studies the stabilization of a class of control systems that use communication networks as signal transmission medium. The lateral motion of independently actuated four-wheel vehicle is modeled as an uncertain-linear system. Time delay and quantization density are modeled as Markov chains.The networked control systems(NCSs) with plants being lateral motion are first transformed to switched linear systems with uncertain parameters. Sufficient and necessary conditions for the stochastic stability of closed-loop networked control systems are then established. By solving the matrix inequalities, this work presents an output-feedback controller that depends on the modes of time delay and quantization density. The controller performance is illustrated via a vehicular lateral motion system.展开更多
A memristor-coupled heterogenous neural network consisting of two-dimensional(2D)FitzHugh–Nagumo(FHN)and Hindmarsh–Rose(HR)neurons with two time delays is established.Taking the time delays as the control parameters...A memristor-coupled heterogenous neural network consisting of two-dimensional(2D)FitzHugh–Nagumo(FHN)and Hindmarsh–Rose(HR)neurons with two time delays is established.Taking the time delays as the control parameters,the existence of Hopf bifurcation near the stable equilibrium point in four cases is derived theoretically,and the validity of the Hopf bifurcation condition is verified by numerical analysis.The results show that the two time delays can make the stable equilibrium point unstable,thus leading to periodic oscillations induced by Hopf bifurcation.Furthermore,the time delays in FHN and HR neurons have different effects on the firing activity of neural network.Complex firing patterns,such as quiescent state,chaotic spiking,and periodic spiking can be induced by the time delay in FHN neuron,while the neural network only exhibits quiescent state and periodic spiking with the change of the time delay in HR neuron.Especially,phase synchronization between the heterogeneous neurons is explored,and the results show that the time delay in HR neurons has a greater effect on blocking the synchronization than the time delay in FHN neuron.Finally,the theoretical analysis is verified by circuit simulations.展开更多
The rapid development of the Internet has broadened the channels of dissemination of information,it has also led to the rapid and widespread propagation of rumors,which can have a serious negative impact socially.In t...The rapid development of the Internet has broadened the channels of dissemination of information,it has also led to the rapid and widespread propagation of rumors,which can have a serious negative impact socially.In this paper,an improved ISR-WV rumor propagation model integrating multichannels is proposed by considering the system’s time delay,and the influence of different channels of propagation on the dynamic process is further analyzed.Moreover,the basic reproduction number R0,rumor-free equilibrium,and rumor-prevailing equilibrium,as well as their stability,are deduced.Then,an optimal control problem with pulse vaccination is designed.Finally,the validity of the model and theoretical results is verified by numerical simulations and a practical application.The results show that the rumor propagation threshold R0 is more sensitive to the rate of the propagation of the information base channel.The shorter the thinking timeτ_(1)required for the ignorant to react after obtaining the information,the larger the final scale of propagation.Under this condition,the time delayτ_(2)spent by a spreader in producing a video is negatively related to the final scale of the propagation;conversely,a longerτ_(1)implies that the person tends to more cognizant,which can suppress the spread of rumors.Under this condition,τ_(2)has little effect on the final scale of propagation.In addition,the results also prove that timely implementation of the pulse vaccination control strategy of popular science education can effectively control the propagation of rumors and reduce their negative impact.展开更多
This paper is devoted to investigate the robust H∞sliding mode load frequency control(SMLFC) of multi-area power system with time delay. By taking into account stochastic disturbances induced by the integration of re...This paper is devoted to investigate the robust H∞sliding mode load frequency control(SMLFC) of multi-area power system with time delay. By taking into account stochastic disturbances induced by the integration of renewable energies,a new sliding surface function is constructed to guarantee the fast response and robust performance, then the sliding mode control law is designed to guarantee the reach ability of the sliding surface in a finite-time interval. The sufficient robust frequency stabilization result for multi-area power system with time delay is presented in terms of linear matrix inequalities(LMIs). Finally,a two-area power system is provided to illustrate the usefulness and effectiveness of the obtained results.展开更多
Noise and time delay are inevitable in real-world networks. In this article, the framework of master stability function is generalized to stochastic complex networks with time-delayed coupling. The focus is on the eff...Noise and time delay are inevitable in real-world networks. In this article, the framework of master stability function is generalized to stochastic complex networks with time-delayed coupling. The focus is on the effects of noise, time delay,and their inner interactions on the network synchronization. It is found that when there exists time-delayed coupling in the network and noise diffuses through all state variables of nodes, appropriately increasing the noise intensity can effectively improve the network synchronizability;otherwise, noise can be either beneficial or harmful. For stochastic networks, large time delays will lead to desynchronization. These findings provide valuable references for designing optimal complex networks in practical applications.展开更多
This paper considers the mean square output containment control problem for heterogeneous multi-agent systems(MASs)with randomly switching topologies and nonuniform distributed delays.By modeling the switching topolog...This paper considers the mean square output containment control problem for heterogeneous multi-agent systems(MASs)with randomly switching topologies and nonuniform distributed delays.By modeling the switching topologies as a continuous-time Markov process and taking the distributed delays into consideration,a novel distributed containment observer is proposed to estimate the convex hull spanned by the leaders'states.A novel distributed output feedback containment controller is then designed without using the prior knowledge of distributed delays.By constructing a novel switching Lyapunov functional,the output containment control problem is then solved in the sense of mean square under an easily-verifiable sufficient condition.Finally,two numerical examples are given to show the effectiveness of the proposed controller.展开更多
In this paper, a sliding mode observer scheme of sensor fault diagnosis is proposed for a class of time delay nonlinear systems with input uncertainty based on neural network. The sensor fault and the system input unc...In this paper, a sliding mode observer scheme of sensor fault diagnosis is proposed for a class of time delay nonlinear systems with input uncertainty based on neural network. The sensor fault and the system input uncertainty are assumed to be unknown but bounded. The radial basis function (RBF) neural network is used to approximate the sensor fault. Based on the output of the RBF neural network, the sliding mode observer is presented. Using the Lyapunov method, a criterion for stability is given in terms of matrix inequality. Finally, an example is given for illustrating the availability of the fault diagnosis based on the proposed sliding mode observer.展开更多
The Noether symmetries and the conserved quantities for generalized Birkhoffian systems with time delay are studied.Firstly,the generalized Pfaff-Birkhoff principle with time delay is proposed,and the generalized Birk...The Noether symmetries and the conserved quantities for generalized Birkhoffian systems with time delay are studied.Firstly,the generalized Pfaff-Birkhoff principle with time delay is proposed,and the generalized Birkhoff's equations with time delay are obtained.Secondly,the generalized Noether quasi-symmetric transformations of the system are defined,and the criterion of the Noether symmetries is established.Then the Noether theorem for generalized Birkhoffian systems with time delay is established.Finally,by imposing restrictions of constraints on the infinitesimal transformations,the Noether theorem of constrained Birkhoffian systems with time delay is established.One example is given to illustrate the application of the results.展开更多
Optical chaos has attracted widespread attention owing to its complex dynamic behaviors.However,the time delay signature(TDS)caused by the external cavity mode reduces the complexity of optical chaos.We propose and nu...Optical chaos has attracted widespread attention owing to its complex dynamic behaviors.However,the time delay signature(TDS)caused by the external cavity mode reduces the complexity of optical chaos.We propose and numerically demonstrate the critical dispersion of chirped fiber Bragg grating(CFBG)for eliminating the TDS of laser chaos in this work.The critical dispersion,as a function of relaxation frequency and bandwidth of the optical spectrum,is found through extensive dynamics simulations.It is shown that the TDS can be eliminated when the dispersion of CFBG is above this critical dispersion.In addition,the influence of dispersive feedback light and output light from a laser is investigated.These results provide important quantitative guidance for designing chaotic semiconductor lasers without TDS.展开更多
To improve the estimation accuracy,a novel time delay estimation(TDE)method based on the closed-form offset compensation is proposed.Firstly,we use the generalized cross-correlation with phase transform(GCC-PHAT)metho...To improve the estimation accuracy,a novel time delay estimation(TDE)method based on the closed-form offset compensation is proposed.Firstly,we use the generalized cross-correlation with phase transform(GCC-PHAT)method to obtain the initial TDE.Secondly,a signal model using normalized cross spectrum is established,and the noise subspace is extracted by eigenvalue decomposition(EVD)of covariance matrix.Using the orthogonal relation between the steering vector and the noise subspace,the first-order Taylor expansion is carried out on the steering vector reconstructed by the initial TDE.Finally,the offsets are compensated via simple least squares(LS).Compared to other state-of-the-art methods,the proposed method significantly reduces the computational complexity and achieves better estimation performance.Experiments on both simulation and real-world data verify the efficiency of the proposed approach.展开更多
The true-time delay(TTD)units are critical for solving beam squint and frequency selective fading inWideband Large-Scale Antenna Systems(LSASs).In this work,we propose a TTD array architecture for wideband multi-beam ...The true-time delay(TTD)units are critical for solving beam squint and frequency selective fading inWideband Large-Scale Antenna Systems(LSASs).In this work,we propose a TTD array architecture for wideband multi-beam tracking that eliminates the beam squint phenomenon and filters out interference signals by applying a spatial filter and time delay estimations(TDEs).The paper presents a novel approach to spatial filter design by introducing a transformation matrix that can optimize the beam response in a specific direction and at a specific frequency.Using the variable fractional delay(VFD)filters,we propose a TDE algorithm with a Newton-Raphson iteration update process that corrects the arrival time delay difference between sensors.Simulations and examples have demonstrated that the proposed architecture can achieve beam tracking within 10 ms at the low signalto-noise ratio(SNR)and demodulation loss is less than 0.5 dB in wideband multi-beam scenarios.展开更多
文摘A study was conducted on the effect of time delay and structural parameters on the vibration reduction of a time delayed coupled negative stiffness dynamic absorber in nonlinear vibration reduction systems. Taking dynamic absorbers with different structural and control parameters as examples, the effects of third-order nonlinear coefficients, time-delay control parameters, and negative stiffness coefficients on reducing the replication of the main system were discussed. The nonlinear dynamic absorber has a very good vibration reduction effect at the resonance point of the main system and a nearby area, and when 1 increases to a certain level, the stable region of the system continues to increase. The amplitude curve of the main system of a nonlinear dynamic absorber will generate Hop bifurcation and saddle node bifurcation in the region far from the resonance point, resulting in almost periodic motion and jumping phenomena in the system. For nonlinear dynamic absorbers with determined structural parameters, time-delay feedback control can be adopted to control the amplitude of the main system. For different negative stiffness coefficients, there exists a minimum damping point for the amplitude of the main system under the determined system structural parameters and time-delay feedback control parameters.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.92150105,11834004,12227807,and 12241407)the Science and Technology Commission of Shanghai Municipality (Grant No.21ZR1420100)。
文摘Electronic processes within atoms and molecules reside on the timescale of attoseconds. Recent advances in the laserbased pump-probe interrogation techniques have made possible the temporal resolution of ultrafast electronic processes on the attosecond timescale, including photoionization and tunneling ionization. These interrogation techniques include the attosecond streak camera, the reconstruction of attosecond beating by interference of two-photon transitions, and the attoclock. While the former two are usually employed to study photoionization processes, the latter is typically used to investigate tunneling ionization. In this review, we briefly overview these timing techniques towards an attosecond temporal resolution of ionization processes in atoms and molecules under intense laser fields. In particular, we review the backpropagation method, which is a novel hybrid quantum-classical approach towards the full characterization of tunneling ionization dynamics. Continued advances in the interrogation techniques promise to pave the pathway towards the exploration of ever faster dynamical processes on an ever shorter timescale.
基金supported in part by the National Natural Science Foundation of China (NSFC)(61703086, 61773106)the IAPI Fundamental Research Funds (2018ZCX27)
文摘This paper is concerned with consensus of a secondorder linear time-invariant multi-agent system in the situation that there exists a communication delay among the agents in the network.A proportional-integral consensus protocol is designed by using delayed and memorized state information.Under the proportional-integral consensus protocol,the consensus problem of the multi-agent system is transformed into the problem of asymptotic stability of the corresponding linear time-invariant time-delay system.Note that the location of the eigenvalues of the corresponding characteristic function of the linear time-invariant time-delay system not only determines the stability of the system,but also plays a critical role in the dynamic performance of the system.In this paper,based on recent results on the distribution of roots of quasi-polynomials,several necessary conditions for Hurwitz stability for a class of quasi-polynomials are first derived.Then allowable regions of consensus protocol parameters are estimated.Some necessary and sufficient conditions for determining effective protocol parameters are provided.The designed protocol can achieve consensus and improve the dynamic performance of the second-order multi-agent system.Moreover,the effects of delays on consensus of systems of harmonic oscillators/double integrators under proportional-integral consensus protocols are investigated.Furthermore,some results on proportional-integral consensus are derived for a class of high-order linear time-invariant multi-agent systems.
基金partially supported by the DEEPCOBOT project under Grant 306640/O70 funded by the Research Council of Norway.
文摘In this paper,we consider a 2-degrees-of-freedom(DOF)helicopter system subject to long input delays and uncertain system parameters.To address the challenges including unknown system parameters and input delays in control design,we develop an adaptive predictor-feedback control law to achieve trajectory tracking.Stability of the closed-loop system is further established,where the tracking errors are shown to converge towards zero.Through simulation and experiments on the helicopter system,we illustrate that tracking of a desired trajectory is achieved with the proposed control scheme.
文摘RSs(Radar Systems)identify and trace targets and are commonly employed in applications like air traffic control and remote sensing.They are necessary for monitoring precise target trajectories.Estimations of RSs are non-linear as the parameters TDEs(time delay Estimations)and Doppler shifts are computed on receipt of echoes where EKFs(Extended Kalman Filters)and UKFs(Unscented Kalman Filters)have not been examined for computations.RSs,certain times result in poor accuracies and SNRs(low signal to noise ratios)especially,while encountering complicated environments.This work proposes IUKFs(Iterated UKFs)to track onlinefilter performances while using optimization techniques to enhance outcomes.The use of cost functions can assist state corrections while lowering costs.A new parameter is optimized using MCEHOs(Mutation Chaotic Elephant Herding Optimizations)by linearly approximating system non-linearity where OIUKFs(Optimized Iterative UKFs)predict a target's unknown parameters.To obtain optimal solutions theoretically,OIUKFs take less iteration,resulting in shorter execution times.The proposed OIUKFs provide numerical approximations which are derivative-free implementations.Simulation evaluation results with estimators show better performances in terms of reduced NMSEs(Normalized Mean Square Errors),RMSEs(Root Mean Squared Errors),SNRs,variances,and better accuracies than current approaches.
文摘Breast cancer in women is a complicated and multifaceted disease. Studies have demonstrated that hyperglycemia is one of the most significant risk factors for breast cancer. Hyperglycemia is when the sugar level in human blood is too high, which means excess glucose. Glucose excess can encourage the growth, invasion, and migration of breast cancer cells at the cellular level. Though, the effects of glucose on the dynamics of breast cancer cells have been examined mathematically by a system of ordinary differential equations. However, the non-instantaneous biological occurrences leading to the secretion of immuno-suppressive cytokines by tumors to evade immune surveillance and the immune cells’ derivation of cytokines to attack the tumor cells are not yet discussed. Therefore, investigating the biological process involved in the dynamics of tumors, immune and normal cells with excessive glucose concentration is inviolable to determining the best procedure for controlling tumors’ uncontrollable growth. Time delay, denoted by τ, is used to describe the time tumor cells take to secrete immunosuppressive cytokines to evade immune surveillance and the time immune cells take to recognize and attack the tumor cells. We have studied the local stability analysis of the biological steady states in both delayed and non-delayed system. The Routh-Hurwitz stability criterion is used to analyze the dynamical equilibrium of the cells’ population. Hopf bifurcation was analyzed by using time delay s as a bifurcation parameter. The analytical results suggest an unstable scenario for a tumor-free equilibrium point as normal cells are bound to grow to their carrying capacity. The result predicts a stable system for coexisting equilibrium when the interaction is instantaneous (τ = 0). However, when τ > 0, the coexisting equilibrium point switches from stable to unstable. The numerical results not only validate all the analytical results but also show the case of possible situations when glucose concentration is varied, indicating that both tumor growth and immune system efficiency are highly affected by the level of glucose in the blood. This concluded that the delay in the secretion of cytokines by immune cells and derivation cytokines by the tumors helps to identify the possible chaotic situation under different glucose concentration and the extent to which such delay can have on restoration of the normal cells when glucose concentration is low.
基金supported by National Natural Science Foundation of China(11371049)
文摘It is an important issue to estimate parameters of fractional-order chaotic systems in nonlinear science, which has received increasing interest in recent years. In this paper, time delay and fractional order as well as system’s parameters are concerned by treating the time delay and fractional order as additional parameters. The parameter estimation is converted into a multi-dimensional optimization problem. A new scheme based on artificial bee colony(ABC) algorithm is proposed to solve the optimization problem. Numerical experiments are performed on two typical time-delay fractional-order chaotic systems to verify the effectiveness of the proposed method.
基金supported by the National Natural Science Foundation of China(61273200,61273152,61202111,61304052,51407088)the Science Foundation of Education Office of Shandong Province of China(ZR2011FM07,BS2015DX018)
文摘In complex environments, many distributed multiagent systems are described with the fractional-order dynamics.In this paper, containment control of fractional-order multiagent systems with multiple leader agents are studied. Firstly,the collaborative control of fractional-order multi-agent systems(FOMAS) with multiple leaders is analyzed in a directed network without delays. Then, by using Laplace transform and frequency domain theorem, containment consensus of networked FOMAS with time delays is investigated in an undirected network, and a critical value of delays is obtained to ensure the containment consensus of FOMAS. Finally, numerical simulations are shown to verify the results.
基金partly supported by the National Key Research and Development Plan Intelligent Robot Key Project(2018YFB1308000)the Key Research and Development Program of Zhejiang Province(2020C01109)。
文摘The stabilization problem of distributed proportional-integral-derivative(PID)controllers for general first-order multi-agent systems with time delay is investigated in the paper.The closed-loop multi-input multi-output(MIMO)framework in frequency domain is firstly introduced for the multi-agent system.Based on the matrix theory,the whole system is decoupled into several subsystems with respect to the eigenvalues of the Laplacian matrix.Considering that the eigenvalues may be complex numbers,the consensus problem of the multi-agent system is transformed into the stabilizing problem of all the subsystems with complex coefficients.For each subsystem with complex coefficients,the range of admissible proportional gains is analytically determined.Then,the stabilizing region in the space of integral gain and derivative gain for a given proportional gain value is also obtained in an analytical form.The entire stabilizing set can be determined by sweeping proportional gain in the allowable range.The proposed method is conducted for general first-order multi-agent systems under arbitrary topology including undirected and directed graph topology.Besides,the results in the paper provide the basis for the design of distributed PID controllers satisfying different performance criteria.The simulation examples are presented to check the validity of the proposed control strategy.
基金supported by Humanities and Social Sciences Youth Foundation of the Ministry of Education(17YJC630093)
文摘This work studies the stabilization of a class of control systems that use communication networks as signal transmission medium. The lateral motion of independently actuated four-wheel vehicle is modeled as an uncertain-linear system. Time delay and quantization density are modeled as Markov chains.The networked control systems(NCSs) with plants being lateral motion are first transformed to switched linear systems with uncertain parameters. Sufficient and necessary conditions for the stochastic stability of closed-loop networked control systems are then established. By solving the matrix inequalities, this work presents an output-feedback controller that depends on the modes of time delay and quantization density. The controller performance is illustrated via a vehicular lateral motion system.
基金the National Natural Science Foundations of China(Grant Nos.62171401 and 62071411).
文摘A memristor-coupled heterogenous neural network consisting of two-dimensional(2D)FitzHugh–Nagumo(FHN)and Hindmarsh–Rose(HR)neurons with two time delays is established.Taking the time delays as the control parameters,the existence of Hopf bifurcation near the stable equilibrium point in four cases is derived theoretically,and the validity of the Hopf bifurcation condition is verified by numerical analysis.The results show that the two time delays can make the stable equilibrium point unstable,thus leading to periodic oscillations induced by Hopf bifurcation.Furthermore,the time delays in FHN and HR neurons have different effects on the firing activity of neural network.Complex firing patterns,such as quiescent state,chaotic spiking,and periodic spiking can be induced by the time delay in FHN neuron,while the neural network only exhibits quiescent state and periodic spiking with the change of the time delay in HR neuron.Especially,phase synchronization between the heterogeneous neurons is explored,and the results show that the time delay in HR neurons has a greater effect on blocking the synchronization than the time delay in FHN neuron.Finally,the theoretical analysis is verified by circuit simulations.
基金This work was partially supported by the Project for the National Natural Science Foundation of China(Grant Nos.72174121 and 71774111)the Program for Professor of Special Appointment(Eastern Scholar)at Shanghai Institutions of Higher Learning,and the Project for the Natural Science Foundation of Shanghai(Grant No.21ZR1444100).
文摘The rapid development of the Internet has broadened the channels of dissemination of information,it has also led to the rapid and widespread propagation of rumors,which can have a serious negative impact socially.In this paper,an improved ISR-WV rumor propagation model integrating multichannels is proposed by considering the system’s time delay,and the influence of different channels of propagation on the dynamic process is further analyzed.Moreover,the basic reproduction number R0,rumor-free equilibrium,and rumor-prevailing equilibrium,as well as their stability,are deduced.Then,an optimal control problem with pulse vaccination is designed.Finally,the validity of the model and theoretical results is verified by numerical simulations and a practical application.The results show that the rumor propagation threshold R0 is more sensitive to the rate of the propagation of the information base channel.The shorter the thinking timeτ_(1)required for the ignorant to react after obtaining the information,the larger the final scale of propagation.Under this condition,the time delayτ_(2)spent by a spreader in producing a video is negatively related to the final scale of the propagation;conversely,a longerτ_(1)implies that the person tends to more cognizant,which can suppress the spread of rumors.Under this condition,τ_(2)has little effect on the final scale of propagation.In addition,the results also prove that timely implementation of the pulse vaccination control strategy of popular science education can effectively control the propagation of rumors and reduce their negative impact.
基金supported in part by the National Natural Science Foundation of China(61673161)the Natural Science Foundation of Jiangsu Province of China(BK20161510)+2 种基金the Fundamental Research Funds for the Central Universities of China(2017B13914)the 111 Project(B14022)the Priority Academic Program Development of Jiangsu Higher Education Institutions(PAPD)
文摘This paper is devoted to investigate the robust H∞sliding mode load frequency control(SMLFC) of multi-area power system with time delay. By taking into account stochastic disturbances induced by the integration of renewable energies,a new sliding surface function is constructed to guarantee the fast response and robust performance, then the sliding mode control law is designed to guarantee the reach ability of the sliding surface in a finite-time interval. The sufficient robust frequency stabilization result for multi-area power system with time delay is presented in terms of linear matrix inequalities(LMIs). Finally,a two-area power system is provided to illustrate the usefulness and effectiveness of the obtained results.
基金Project supported in part by the National Natural Science Foundation of China (Grant No. 61973064)the Natural Science Foundation of Hebei Province of China (Grant Nos. F2019501126 and F2022501024)+1 种基金the Natural Science Foundation of Liaoning Province, China (Grant No. 2020-KF11-03)the Fund from Hong Kong Research Grants Council (Grant No. CityU11206320)。
文摘Noise and time delay are inevitable in real-world networks. In this article, the framework of master stability function is generalized to stochastic complex networks with time-delayed coupling. The focus is on the effects of noise, time delay,and their inner interactions on the network synchronization. It is found that when there exists time-delayed coupling in the network and noise diffuses through all state variables of nodes, appropriately increasing the noise intensity can effectively improve the network synchronizability;otherwise, noise can be either beneficial or harmful. For stochastic networks, large time delays will lead to desynchronization. These findings provide valuable references for designing optimal complex networks in practical applications.
文摘This paper considers the mean square output containment control problem for heterogeneous multi-agent systems(MASs)with randomly switching topologies and nonuniform distributed delays.By modeling the switching topologies as a continuous-time Markov process and taking the distributed delays into consideration,a novel distributed containment observer is proposed to estimate the convex hull spanned by the leaders'states.A novel distributed output feedback containment controller is then designed without using the prior knowledge of distributed delays.By constructing a novel switching Lyapunov functional,the output containment control problem is then solved in the sense of mean square under an easily-verifiable sufficient condition.Finally,two numerical examples are given to show the effectiveness of the proposed controller.
基金Natural Science Foundation of Jiangsu Province (No.SBK20082815)Aeronautical Science Foundation of China (No.20075152014)
文摘In this paper, a sliding mode observer scheme of sensor fault diagnosis is proposed for a class of time delay nonlinear systems with input uncertainty based on neural network. The sensor fault and the system input uncertainty are assumed to be unknown but bounded. The radial basis function (RBF) neural network is used to approximate the sensor fault. Based on the output of the RBF neural network, the sliding mode observer is presented. Using the Lyapunov method, a criterion for stability is given in terms of matrix inequality. Finally, an example is given for illustrating the availability of the fault diagnosis based on the proposed sliding mode observer.
基金supported by the National Natural Science Foundations of China(Nos.11572212,11272227)
文摘The Noether symmetries and the conserved quantities for generalized Birkhoffian systems with time delay are studied.Firstly,the generalized Pfaff-Birkhoff principle with time delay is proposed,and the generalized Birkhoff's equations with time delay are obtained.Secondly,the generalized Noether quasi-symmetric transformations of the system are defined,and the criterion of the Noether symmetries is established.Then the Noether theorem for generalized Birkhoffian systems with time delay is established.Finally,by imposing restrictions of constraints on the infinitesimal transformations,the Noether theorem of constrained Birkhoffian systems with time delay is established.One example is given to illustrate the application of the results.
基金the National Natural Science Foundation of China(Grant No.62105190)the Natural Science Foundation of Shanxi Province of China(Grant No.20210302124268)+1 种基金the Scientific and Technological Innovation Programs of Higher Education Institutions of Shanxi Province of China(Grant No.2021L285)the Youth Researchof Shanxi University of Finance and Economics(Grant No.QN-202015)。
文摘Optical chaos has attracted widespread attention owing to its complex dynamic behaviors.However,the time delay signature(TDS)caused by the external cavity mode reduces the complexity of optical chaos.We propose and numerically demonstrate the critical dispersion of chirped fiber Bragg grating(CFBG)for eliminating the TDS of laser chaos in this work.The critical dispersion,as a function of relaxation frequency and bandwidth of the optical spectrum,is found through extensive dynamics simulations.It is shown that the TDS can be eliminated when the dispersion of CFBG is above this critical dispersion.In addition,the influence of dispersive feedback light and output light from a laser is investigated.These results provide important quantitative guidance for designing chaotic semiconductor lasers without TDS.
基金supported in part by National Key R&D Program of China under Grants 2020YFB1807602 and 2020YFB1807600National Science Foundation of China(61971217,61971218,61631020,61601167)+1 种基金the Fund of Sonar Technology Key Laboratory(Range estimation and location technology of passive target viamultiple array combination),Jiangsu Planned Projects for Postdoctoral Research Funds(2020Z013)China Postdoctoral Science Foundation(2020M681585).
文摘To improve the estimation accuracy,a novel time delay estimation(TDE)method based on the closed-form offset compensation is proposed.Firstly,we use the generalized cross-correlation with phase transform(GCC-PHAT)method to obtain the initial TDE.Secondly,a signal model using normalized cross spectrum is established,and the noise subspace is extracted by eigenvalue decomposition(EVD)of covariance matrix.Using the orthogonal relation between the steering vector and the noise subspace,the first-order Taylor expansion is carried out on the steering vector reconstructed by the initial TDE.Finally,the offsets are compensated via simple least squares(LS).Compared to other state-of-the-art methods,the proposed method significantly reduces the computational complexity and achieves better estimation performance.Experiments on both simulation and real-world data verify the efficiency of the proposed approach.
基金supported by the foundation of National Key Laboratory of Electromagnetic Environment(Grant No.202103012).
文摘The true-time delay(TTD)units are critical for solving beam squint and frequency selective fading inWideband Large-Scale Antenna Systems(LSASs).In this work,we propose a TTD array architecture for wideband multi-beam tracking that eliminates the beam squint phenomenon and filters out interference signals by applying a spatial filter and time delay estimations(TDEs).The paper presents a novel approach to spatial filter design by introducing a transformation matrix that can optimize the beam response in a specific direction and at a specific frequency.Using the variable fractional delay(VFD)filters,we propose a TDE algorithm with a Newton-Raphson iteration update process that corrects the arrival time delay difference between sensors.Simulations and examples have demonstrated that the proposed architecture can achieve beam tracking within 10 ms at the low signalto-noise ratio(SNR)and demodulation loss is less than 0.5 dB in wideband multi-beam scenarios.
