Chaos synchronization of coupled nonlinear systems is ubiquitous in nature and science. Dynamic behaviors of coupled ring and linear arrays of unidirectionally coupled Lorenz oscillators are studied numerically. We fi...Chaos synchronization of coupled nonlinear systems is ubiquitous in nature and science. Dynamic behaviors of coupled ring and linear arrays of unidirectionally coupled Lorenz oscillators are studied numerically. We find that chaos synchronization in circular arrays of chaotic systems can occur through the on off intermittent synchronization with a power law distribution of laminar phases. And in the coupled ring and linear array it is found that the chaotic rotating waves generated from the ring propagate with spatial periodic synchronization along the linear array.展开更多
This paper proposes a method of realizing generalized chaos synchronization of a weighted complex network with different nodes. Chaotic systems with diverse structures are taken as the nodes of the complex dynamical n...This paper proposes a method of realizing generalized chaos synchronization of a weighted complex network with different nodes. Chaotic systems with diverse structures are taken as the nodes of the complex dynamical network, the nonlinear terms of the systems are taken as coupling functions, and the relations among the nodes are built through weighted connections. The structure of the coupling functions between the connected nodes is obtained based on Lyapunov stability theory. A complex network with nodes of Lorenz system, Coullet system, RSssler system and the New system is taken as an example for simulation study and the results show that generalized chaos synchronization exists in the whole weighted complex network with different nodes when the coupling strength among the nodes is given with any weight value. The method can be used in realizing generalized chaos synchronization of a weighted complex network with different nodes. Furthermore, both the weight value of the coupling strength among the nodes and the number of the nodes have no effect on the stability of synchronization in the whole complex network.展开更多
Using the properties of chaos synchronization, the method for estimating the largest Lyapunov exponent in a multibody system with dry friction is presented in this paper. The Lagrange equations with multipliers of the...Using the properties of chaos synchronization, the method for estimating the largest Lyapunov exponent in a multibody system with dry friction is presented in this paper. The Lagrange equations with multipliers of the systems are given in matrix form, which is adequate for numerical calculation. The approach for calculating the generalized velocity and acceleration of the slider is given to determine slipping or sticking of the slider in the systems. For slip-slip and stick-slip multibody systems, their largest Lyapunov exponents are calculated to characterize their dynamics.展开更多
Based on the rate equations, we have investigated three types of chaos synchronizations in injection-locked semiconductor lasers with optical feedback. Numerical simulation shows that the synchronization can be realiz...Based on the rate equations, we have investigated three types of chaos synchronizations in injection-locked semiconductor lasers with optical feedback. Numerical simulation shows that the synchronization can be realized by the symmetric or asymmetric laser systems. Also, the influence of parameter mismatches on chaos synchronization is investigated, and the results imply that these two lasers can achieve good synchronization, with smaller tolerance of parameter mismatch existing.展开更多
In this paper, the asymptotical p-moment stability of stochastic impulsive differential equations is studied and a comparison theory to ensure the asymptotical p-moment stability of the trivial solution is established...In this paper, the asymptotical p-moment stability of stochastic impulsive differential equations is studied and a comparison theory to ensure the asymptotical p-moment stability of the trivial solution is established, which is important for studying the impulsive control and synchronization in stochastic systems. As an application of this theory, we study the problem of chaos synchronization in the Chen system excited by parameter white-noise excitation, by using the impulsive method. Numerical simulations verify the feasibility of this method.展开更多
In this paper, chaos synchronization in the presence of parameter uncertainty, observer gain perturbation and exogenous input disturbance is considered. A nonlinear non-fragile proportional-integral （PI） adaptive ob...In this paper, chaos synchronization in the presence of parameter uncertainty, observer gain perturbation and exogenous input disturbance is considered. A nonlinear non-fragile proportional-integral （PI） adaptive observer is designed for the synchronization of chaotic systems; its stability conditions based on the Lyapunov technique are derived. The observer proportional and integral gains, by converting the conditions into linear matrix inequality （LMI）, are optimally selected from solutions that satisfy the observer stability conditions such that the effect of disturbance on the synchronization error becomes minimized. To show the effectiveness of the proposed method, simulation results for the synchronization of a Lorenz chaotic system with unknown parameters in the presence of an exogenous input disturbance and abrupt gain perturbation are reported.展开更多
This paper presents chaos synchronization between two different four-dimensional （4D） hyperchaotic Chen systems by nonlinear feedback control laws. A modified 4D hyperchaotic Chen system is obtained by changing the ...This paper presents chaos synchronization between two different four-dimensional （4D） hyperchaotic Chen systems by nonlinear feedback control laws. A modified 4D hyperchaotic Chen system is obtained by changing the nonlinear function of the 4D hyperchaotic Chen system, furthermore, an electronic circuit to realize two different 4D hyperchaotic Chen systems is designed. With nonlinear feedback control method, chaos synchronization between two different 4D hyperchaotic Chen systems is achieved. Based on the stability theory~ the functions of the nonlinear feedback control for synchronization of two different 4D hyperchaotic Chen systems is derived, the range of feedback gains is determined. Numerical simulations are shown to verify the theoretical results.展开更多
To design a hyperchaotic generator and apply chaos into secure communication, a linear unidirectional coupling control is applied to two identical simplified Lorenz systems. The dynamical evolution process of the coup...To design a hyperchaotic generator and apply chaos into secure communication, a linear unidirectional coupling control is applied to two identical simplified Lorenz systems. The dynamical evolution process of the coupled system is investigated with variations of the system parameter and coupling coefficients. Particularly, the influence of coupling strength on dynamics of the coupled system is analyzed in detail. The range of the coupling strength in which the coupled system can generate hyperchaos or realize synchronization is determined, including phase portraits, Lyapunov exponents, and Poincare section. And the critical value of the system parameter between hyperchaos and synchronization is also found with fixed coupled strength. In addition, abundant dynamical behaviors such as four-wing hyperchaotic, two-wing chaotic, single-wing coexisting attractors and periodic orbits are observed and chaos synchronization error curves are also drawn by varying system parameter c. Numerical simulations are implemented to verify the results of these investigations.展开更多
As an important research branch,memristor has attracted a range of scholars to study the property of memristive chaotic systems.Additionally,time⁃delayed systems are considered a significant and newly⁃developing field...As an important research branch,memristor has attracted a range of scholars to study the property of memristive chaotic systems.Additionally,time⁃delayed systems are considered a significant and newly⁃developing field in modern research.By combining memristor and time⁃delay,a delayed memristive differential system with fractional order is proposed in this paper,which can generate hidden attractors.First,we discussed the dynamics of the proposed system where the parameter was set as the bifurcation parameter,and showed that with the increase of the parameter,the system generated rich chaotic phenomena such as bifurcation,chaos,and hypherchaos.Then we derived adequate and appropriate stability criteria to guarantee the system to achieve synchronization.Lastly,examples were provided to analyze and confirm the influence of parameter a,fractional order q,and time delayτon chaos synchronization.The simulation results confirm that the chaotic synchronization is affected by a,q andτ.展开更多
In this paper, based on an adaptive chaos synchronization scheme, two methods of encoding-decoding message for secure communication are proposed. With the first method, message is directly added to the chaotic signal ...In this paper, based on an adaptive chaos synchronization scheme, two methods of encoding-decoding message for secure communication are proposed. With the first method, message is directly added to the chaotic signal with parameter uncertainty. In the second method, multi-parameter modulation is used to simultaneously transmit more than one digital message （i.e., the multichannel digital communication） through just a single signal, which switches among various chaotic attractors that differ only subtly. In theory, such a treatment increases the difficulty for the intruder to directly intercept the information, and meanwhile the implementation cost decreases significantly. In addition, numerical results show the methods are robust against weak noise, which implies their practicability.展开更多
Based on a generalized chaos synchronization system and a discrete Sinai map, a non-symmetric true color （RGB） digital image secure communication scheme is proposed. The scheme first changes an ordinary RGB digital ...Based on a generalized chaos synchronization system and a discrete Sinai map, a non-symmetric true color （RGB） digital image secure communication scheme is proposed. The scheme first changes an ordinary RGB digital image with 8 bits into unrecognizable disorder codes and then transforms the disorder codes into an RGB digital image with 16 bits for transmitting. A receiver uses a non-symmetric key to verify the authentication of the received data origin, and decrypts the ciphertext. The scheme can encrypt and decz：Fpt most formatted digital RGB images recognized by computers, and recover the plaintext almost without any errors. The scheme is suitable to be applied in network image communications. The analysis of the key space, sensitivity of key parameters, and correlation of encrypted images imply that this scheme has sound security.展开更多
In this paper, we propose a new input-to-state stable （ISS） synchronization method for chaotic behavior in nonlinear Bloch equations with external disturbance. Based on Lyapunov theory and linear matrix inequality ...In this paper, we propose a new input-to-state stable （ISS） synchronization method for chaotic behavior in nonlinear Bloch equations with external disturbance. Based on Lyapunov theory and linear matrix inequality （LMI） approach, for the first time, the ISS synchronization controller is presented to not only guarantee the asymptotic synchronization but also achieve the bounded synchronization error for any bounded disturbance. The proposed controller can be obtained by solving a convex optimization problem represented by the LMI. Simulation study is presented to demonstrate the effectiveness of the proposed synchronization scheme.展开更多
The sliding mode control method is used to study spatiotemporal chaos synchronization of an uncertain network.The method is extended from synchronization between two chaotic systems to the synchronization of complex n...The sliding mode control method is used to study spatiotemporal chaos synchronization of an uncertain network.The method is extended from synchronization between two chaotic systems to the synchronization of complex network composed of N spatiotemporal chaotic systems.The sliding surface of the network and the control input are designed.Furthermore,the effectiveness of the method is analysed based on the stability theory.The Burgers equation with spatiotemporal chaos behavior is taken as an example to simulate the experiment.It is found that the synchronization performance of the network is very stable.展开更多
The mechanical horizontal platform(MHP)system exhibits a rich chaotic behavior.The chaotic MHP system has applications in the earthquake and offshore industries.This article proposes a robust adaptive continuous contr...The mechanical horizontal platform(MHP)system exhibits a rich chaotic behavior.The chaotic MHP system has applications in the earthquake and offshore industries.This article proposes a robust adaptive continuous control(RACC)algorithm.It investigates the control and synchronization of chaos in the uncertain MHP system with time-delay in the presence of unknown state-dependent and time-dependent disturbances.The closed-loop system contains most of the nonlinear terms that enhance the complexity of the dynamical system;it improves the efficiency of the closed-loop.The proposed RACC approach(a)accomplishes faster convergence of the perturbed state variables(synchronization errors)to the desired steady-state,(b)eradicates the effect of unknown state-dependent and time-dependent disturbances,and(c)suppresses undesirable chattering in the feedback control inputs.This paper describes a detailed closed-loop stability analysis based on the Lyapunov-Krasovskii functional theory and Lyapunov stability technique.It provides parameter adaptation laws that confirm the convergence of the uncertain parameters to some constant values.The computer simulation results endorse the theoretical findings and provide a comparative performance.展开更多
Chaos synchronization of Chen chaotic system for parameters unknown isdiscussed in this paper using a scalar output. Using the concept of conditional Lyapunov exponents,the negativity of all Lyapunov exponents shows t...Chaos synchronization of Chen chaotic system for parameters unknown isdiscussed in this paper using a scalar output. Using the concept of conditional Lyapunov exponents,the negativity of all Lyapunov exponents shows the synchronization of transmitter systems withreceiver systems even though system parametes are not known to receiver systems.展开更多
While the significance of oscillator dynamics and coupling structure to synchronization behaviors has been well addressed in the literature, little attention has been paid to the possible influence of coupling functio...While the significance of oscillator dynamics and coupling structure to synchronization behaviors has been well addressed in the literature, little attention has been paid to the possible influence of coupling functions. In the present paper, adopting the scheme of dual-channel time-delayed couplings, we investigate how the synchronization behaviors of networked chaotic oscillators are influenced by parameters in the coupling functions. It is found that, with the introduction of the second coupling channel, the synchronization region, as calculated according to the method of master stability function(MSF), can be largely modified. In particular, by a slight change of the time delay, it is found that the synchronization region can be significantly adjusted, or even switched from non-existing to existing. We demonstrate this interesting phenomenon for both situations of processing and propagation induced time delays, as well as for different coupling functions. Our studies shed new light on the mechanism of chaos synchronization, and may potentially be used for the control of complex network dynamics.展开更多
We present a scheme for chaotic synchronization in two resistive- capacitive-inductive shunted Josephson junctions （RCLSJJs） by using another chaotic RCLSJJ as a driving system. Numerical simulations show that wheth...We present a scheme for chaotic synchronization in two resistive- capacitive-inductive shunted Josephson junctions （RCLSJJs） by using another chaotic RCLSJJ as a driving system. Numerical simulations show that whether the two RCLSJJs are chaotic or not before being driven, they can realize chaotic synchronization with a suitable driving intensity, under which the maximum condition Lyapunov exponent （MCLE） is negative. On the other hand, if the driving system is in different periodic states or chaotic states, the two driven RCLSJJs can be controlled into the periodic states with different period numbers or chaotic states but still maintain the synchronization.展开更多
In this paper, a new image encryption scheme is presented based on time-delay chaos synchronization. Compared with existing methods, a new method is pro- posed and a lot of coupled items can be taken as zero items to ...In this paper, a new image encryption scheme is presented based on time-delay chaos synchronization. Compared with existing methods, a new method is pro- posed and a lot of coupled items can be taken as zero items to simplify the whole system. A simple linear controller is introduced to realize time-delay chaos synchronization and image encryption. The positions of the image pixels are firstly shuffled and then be hidden in the cartier image. The address codes of the chaotic sequences are adopted to avoid the disturbances induced by the initial value and computer accuracy error. Simulation results for color image are provided to illustrate the effectiveness of the proposed method. It can be seen clearly that the system can converge quickly and the image can be encrypted rapidly.展开更多
The Radial Basis Functions Neural Network （RBFNN） is used to establish the model of a response system through the input and output data of the system. The synchronization between a drive system and the response syst...The Radial Basis Functions Neural Network （RBFNN） is used to establish the model of a response system through the input and output data of the system. The synchronization between a drive system and the response system can be implemented by employing the RBFNN model and state feedback control. In this case, the exact mathematical model, which is the precondition for the conventional method, is unnecessary for implementing synchronization. The effect of the model error is investigated and a corresponding theorem is developed. The effect of the parameter perturbations and the measurement noise is investigated through simulations. The simulation results under different conditions show the effectiveness of the method.展开更多
Synchronization and adaptive synchronization of Morse oscillator with periodic forced section is investigated in this paper. Backstepping design is a recursive procedure that combines the choice of Lyapunov function w...Synchronization and adaptive synchronization of Morse oscillator with periodic forced section is investigated in this paper. Backstepping design is a recursive procedure that combines the choice of Lyapunov function with the design of controller. The proposed approaches offers a syetematic design procedure for synchronization and adaptive synchronization of a large class of continuous-time chaotic systems in the chaos research literature. Simulation results are presented to show the effectiveness of the approaches.展开更多
文摘Chaos synchronization of coupled nonlinear systems is ubiquitous in nature and science. Dynamic behaviors of coupled ring and linear arrays of unidirectionally coupled Lorenz oscillators are studied numerically. We find that chaos synchronization in circular arrays of chaotic systems can occur through the on off intermittent synchronization with a power law distribution of laminar phases. And in the coupled ring and linear array it is found that the chaotic rotating waves generated from the ring propagate with spatial periodic synchronization along the linear array.
基金Project supported by the Natural Science Foundation of Liaoning Province,China(Grant No.20082147)the Innovative Team Program of Liaoning Educational Committee,China(Grant No.2008T108)
文摘This paper proposes a method of realizing generalized chaos synchronization of a weighted complex network with different nodes. Chaotic systems with diverse structures are taken as the nodes of the complex dynamical network, the nonlinear terms of the systems are taken as coupling functions, and the relations among the nodes are built through weighted connections. The structure of the coupling functions between the connected nodes is obtained based on Lyapunov stability theory. A complex network with nodes of Lorenz system, Coullet system, RSssler system and the New system is taken as an example for simulation study and the results show that generalized chaos synchronization exists in the whole weighted complex network with different nodes when the coupling strength among the nodes is given with any weight value. The method can be used in realizing generalized chaos synchronization of a weighted complex network with different nodes. Furthermore, both the weight value of the coupling strength among the nodes and the number of the nodes have no effect on the stability of synchronization in the whole complex network.
基金The project supported by the National Natural Science Foundation of China (10272008 and 10371030)The English text was polished by Yunming Chen
文摘Using the properties of chaos synchronization, the method for estimating the largest Lyapunov exponent in a multibody system with dry friction is presented in this paper. The Lagrange equations with multipliers of the systems are given in matrix form, which is adequate for numerical calculation. The approach for calculating the generalized velocity and acceleration of the slider is given to determine slipping or sticking of the slider in the systems. For slip-slip and stick-slip multibody systems, their largest Lyapunov exponents are calculated to characterize their dynamics.
文摘Based on the rate equations, we have investigated three types of chaos synchronizations in injection-locked semiconductor lasers with optical feedback. Numerical simulation shows that the synchronization can be realized by the symmetric or asymmetric laser systems. Also, the influence of parameter mismatches on chaos synchronization is investigated, and the results imply that these two lasers can achieve good synchronization, with smaller tolerance of parameter mismatch existing.
基金Project supported by the National Natural Science Foundation of China (Grant No. 10872165)
文摘In this paper, the asymptotical p-moment stability of stochastic impulsive differential equations is studied and a comparison theory to ensure the asymptotical p-moment stability of the trivial solution is established, which is important for studying the impulsive control and synchronization in stochastic systems. As an application of this theory, we study the problem of chaos synchronization in the Chen system excited by parameter white-noise excitation, by using the impulsive method. Numerical simulations verify the feasibility of this method.
文摘In this paper, chaos synchronization in the presence of parameter uncertainty, observer gain perturbation and exogenous input disturbance is considered. A nonlinear non-fragile proportional-integral （PI） adaptive observer is designed for the synchronization of chaotic systems; its stability conditions based on the Lyapunov technique are derived. The observer proportional and integral gains, by converting the conditions into linear matrix inequality （LMI）, are optimally selected from solutions that satisfy the observer stability conditions such that the effect of disturbance on the synchronization error becomes minimized. To show the effectiveness of the proposed method, simulation results for the synchronization of a Lorenz chaotic system with unknown parameters in the presence of an exogenous input disturbance and abrupt gain perturbation are reported.
基金Project supported by the National Natural Science Foundation of China （Grant No 90405011）, the Natural Science Foundation of Jiangsu Province, China （Grant No 05KJD120083） and the Natural Science Foundation of Nanjing Institute of Technology, China （Grant No KXJ06047）.
文摘This paper presents chaos synchronization between two different four-dimensional （4D） hyperchaotic Chen systems by nonlinear feedback control laws. A modified 4D hyperchaotic Chen system is obtained by changing the nonlinear function of the 4D hyperchaotic Chen system, furthermore, an electronic circuit to realize two different 4D hyperchaotic Chen systems is designed. With nonlinear feedback control method, chaos synchronization between two different 4D hyperchaotic Chen systems is achieved. Based on the stability theory~ the functions of the nonlinear feedback control for synchronization of two different 4D hyperchaotic Chen systems is derived, the range of feedback gains is determined. Numerical simulations are shown to verify the theoretical results.
基金Projects(61073187,61161006) supported by the National Nature Science Foundation of ChinaProject supported by the Scientific Research Foundation for the Returned Overseas Chinese Scholars,State Education Ministry,China
文摘To design a hyperchaotic generator and apply chaos into secure communication, a linear unidirectional coupling control is applied to two identical simplified Lorenz systems. The dynamical evolution process of the coupled system is investigated with variations of the system parameter and coupling coefficients. Particularly, the influence of coupling strength on dynamics of the coupled system is analyzed in detail. The range of the coupling strength in which the coupled system can generate hyperchaos or realize synchronization is determined, including phase portraits, Lyapunov exponents, and Poincare section. And the critical value of the system parameter between hyperchaos and synchronization is also found with fixed coupled strength. In addition, abundant dynamical behaviors such as four-wing hyperchaotic, two-wing chaotic, single-wing coexisting attractors and periodic orbits are observed and chaos synchronization error curves are also drawn by varying system parameter c. Numerical simulations are implemented to verify the results of these investigations.
基金Sponsored by the National Natural Science Foundation of China(Grant No.61201227)the Funding of China Scholarship Council,the Natural Science the Foundation of Anhui Province(Grant No.1208085M F93)the 211 Innovation Team of Anhui University(Grant Nos.KJTD007A and KJTD001B)
文摘As an important research branch,memristor has attracted a range of scholars to study the property of memristive chaotic systems.Additionally,time⁃delayed systems are considered a significant and newly⁃developing field in modern research.By combining memristor and time⁃delay,a delayed memristive differential system with fractional order is proposed in this paper,which can generate hidden attractors.First,we discussed the dynamics of the proposed system where the parameter was set as the bifurcation parameter,and showed that with the increase of the parameter,the system generated rich chaotic phenomena such as bifurcation,chaos,and hypherchaos.Then we derived adequate and appropriate stability criteria to guarantee the system to achieve synchronization.Lastly,examples were provided to analyze and confirm the influence of parameter a,fractional order q,and time delayτon chaos synchronization.The simulation results confirm that the chaotic synchronization is affected by a,q andτ.
基金Project supported by the National Natural Science Foundation of China （Grant No. 10572080）, Shanghai Rising-Star Program （Grant No.05QMX1422）, and Dawn Project of the Science Foundation of Shanghai Municipal Commission of Education （Grant No.05SG41 04YQHB089）
文摘In this paper, based on an adaptive chaos synchronization scheme, two methods of encoding-decoding message for secure communication are proposed. With the first method, message is directly added to the chaotic signal with parameter uncertainty. In the second method, multi-parameter modulation is used to simultaneously transmit more than one digital message （i.e., the multichannel digital communication） through just a single signal, which switches among various chaotic attractors that differ only subtly. In theory, such a treatment increases the difficulty for the intruder to directly intercept the information, and meanwhile the implementation cost decreases significantly. In addition, numerical results show the methods are robust against weak noise, which implies their practicability.
基金the National Natural Science Foundation of China under，the Foundation for University Key Teachers，高等学校博士学科点专项科研项目，教育部科学技术研究项目
文摘Based on a generalized chaos synchronization system and a discrete Sinai map, a non-symmetric true color （RGB） digital image secure communication scheme is proposed. The scheme first changes an ordinary RGB digital image with 8 bits into unrecognizable disorder codes and then transforms the disorder codes into an RGB digital image with 16 bits for transmitting. A receiver uses a non-symmetric key to verify the authentication of the received data origin, and decrypts the ciphertext. The scheme can encrypt and decz：Fpt most formatted digital RGB images recognized by computers, and recover the plaintext almost without any errors. The scheme is suitable to be applied in network image communications. The analysis of the key space, sensitivity of key parameters, and correlation of encrypted images imply that this scheme has sound security.
文摘In this paper, we propose a new input-to-state stable （ISS） synchronization method for chaotic behavior in nonlinear Bloch equations with external disturbance. Based on Lyapunov theory and linear matrix inequality （LMI） approach, for the first time, the ISS synchronization controller is presented to not only guarantee the asymptotic synchronization but also achieve the bounded synchronization error for any bounded disturbance. The proposed controller can be obtained by solving a convex optimization problem represented by the LMI. Simulation study is presented to demonstrate the effectiveness of the proposed synchronization scheme.
基金Project supported by the Natural Science Foundation of Liaoning Province,China (Grant No. 20082147)the Innovative Team Program of Liaoning Educational Committee,China (Grant No. 2008T108)
文摘The sliding mode control method is used to study spatiotemporal chaos synchronization of an uncertain network.The method is extended from synchronization between two chaotic systems to the synchronization of complex network composed of N spatiotemporal chaotic systems.The sliding surface of the network and the control input are designed.Furthermore,the effectiveness of the method is analysed based on the stability theory.The Burgers equation with spatiotemporal chaos behavior is taken as an example to simulate the experiment.It is found that the synchronization performance of the network is very stable.
文摘The mechanical horizontal platform(MHP)system exhibits a rich chaotic behavior.The chaotic MHP system has applications in the earthquake and offshore industries.This article proposes a robust adaptive continuous control(RACC)algorithm.It investigates the control and synchronization of chaos in the uncertain MHP system with time-delay in the presence of unknown state-dependent and time-dependent disturbances.The closed-loop system contains most of the nonlinear terms that enhance the complexity of the dynamical system;it improves the efficiency of the closed-loop.The proposed RACC approach(a)accomplishes faster convergence of the perturbed state variables(synchronization errors)to the desired steady-state,(b)eradicates the effect of unknown state-dependent and time-dependent disturbances,and(c)suppresses undesirable chattering in the feedback control inputs.This paper describes a detailed closed-loop stability analysis based on the Lyapunov-Krasovskii functional theory and Lyapunov stability technique.It provides parameter adaptation laws that confirm the convergence of the uncertain parameters to some constant values.The computer simulation results endorse the theoretical findings and provide a comparative performance.
文摘Chaos synchronization of Chen chaotic system for parameters unknown isdiscussed in this paper using a scalar output. Using the concept of conditional Lyapunov exponents,the negativity of all Lyapunov exponents shows the synchronization of transmitter systems withreceiver systems even though system parametes are not known to receiver systems.
基金supported by the National Natural Science Foundation of China(Grant No.40976114)the Fundamental Research Funds for the Central Universities(Grant No.GK201303002)
文摘While the significance of oscillator dynamics and coupling structure to synchronization behaviors has been well addressed in the literature, little attention has been paid to the possible influence of coupling functions. In the present paper, adopting the scheme of dual-channel time-delayed couplings, we investigate how the synchronization behaviors of networked chaotic oscillators are influenced by parameters in the coupling functions. It is found that, with the introduction of the second coupling channel, the synchronization region, as calculated according to the method of master stability function(MSF), can be largely modified. In particular, by a slight change of the time delay, it is found that the synchronization region can be significantly adjusted, or even switched from non-existing to existing. We demonstrate this interesting phenomenon for both situations of processing and propagation induced time delays, as well as for different coupling functions. Our studies shed new light on the mechanism of chaos synchronization, and may potentially be used for the control of complex network dynamics.
文摘We present a scheme for chaotic synchronization in two resistive- capacitive-inductive shunted Josephson junctions （RCLSJJs） by using another chaotic RCLSJJ as a driving system. Numerical simulations show that whether the two RCLSJJs are chaotic or not before being driven, they can realize chaotic synchronization with a suitable driving intensity, under which the maximum condition Lyapunov exponent （MCLE） is negative. On the other hand, if the driving system is in different periodic states or chaotic states, the two driven RCLSJJs can be controlled into the periodic states with different period numbers or chaotic states but still maintain the synchronization.
基金Acknowledgments Supported by the National Natural Science Foundation of China （Grant Nos. 51375293, 31570998）, and the Science and Technology Commission of Shanghai Municipality （Grant No. 16511108600）.
文摘In this paper, a new image encryption scheme is presented based on time-delay chaos synchronization. Compared with existing methods, a new method is pro- posed and a lot of coupled items can be taken as zero items to simplify the whole system. A simple linear controller is introduced to realize time-delay chaos synchronization and image encryption. The positions of the image pixels are firstly shuffled and then be hidden in the cartier image. The address codes of the chaotic sequences are adopted to avoid the disturbances induced by the initial value and computer accuracy error. Simulation results for color image are provided to illustrate the effectiveness of the proposed method. It can be seen clearly that the system can converge quickly and the image can be encrypted rapidly.
基金This project was supported in part by the Science Foundation of Shanxi Province (2003F028)China Postdoctoral Science Foundation (20060390318).
文摘The Radial Basis Functions Neural Network （RBFNN） is used to establish the model of a response system through the input and output data of the system. The synchronization between a drive system and the response system can be implemented by employing the RBFNN model and state feedback control. In this case, the exact mathematical model, which is the precondition for the conventional method, is unnecessary for implementing synchronization. The effect of the model error is investigated and a corresponding theorem is developed. The effect of the parameter perturbations and the measurement noise is investigated through simulations. The simulation results under different conditions show the effectiveness of the method.
基金This work is supported by Research Fund Project of Heze University under Grant: XY05SX01.
文摘Synchronization and adaptive synchronization of Morse oscillator with periodic forced section is investigated in this paper. Backstepping design is a recursive procedure that combines the choice of Lyapunov function with the design of controller. The proposed approaches offers a syetematic design procedure for synchronization and adaptive synchronization of a large class of continuous-time chaotic systems in the chaos research literature. Simulation results are presented to show the effectiveness of the approaches.
