The utilization of thin plate systems based on acoustic vibration holds significant importance in micro-nano manipulation and the exploration of nonlinear science. This paper focuses on the analysis of an actual thin ...The utilization of thin plate systems based on acoustic vibration holds significant importance in micro-nano manipulation and the exploration of nonlinear science. This paper focuses on the analysis of an actual thin plate system driven by acoustic wave signals. By combining the mechanical analysis of thin plate microelements with the Bubnov–Galerkin integral method, the governing equation for the forced vibration of a square thin plate is derived. Notably,the reaction force of the thin plate vibration system is defined as f=α|w|, resembling Hooke’s law. The energy function and energy level curve of the system are also analyzed. Subsequently, the amplitude–frequency response function of the thin plate oscillator is solved using the harmonic balance method. Through numerical simulations, the amplitude–frequency curves are analyzed for different vibration modes under the influence of various parameters. Furthermore, the paper demonstrates the occurrence of conservative chaotic motions in the thin plate oscillator using theoretical and numerical methods. Dynamics maps illustrating the system’s states are presented to reveal the evolution laws of the system. By exploring the effects of force fields and system energy, the underlying mechanism of chaos is interpreted. Additionally, the phenomenon of chaos in the oscillator can be controlled through the method of velocity and displacement states feedback, which holds significance for engineering applications.展开更多
This study proposes a novel fractional discrete-time macroeconomic system with incommensurate order.The dynamical behavior of the proposed macroeconomic model is investigated analytically and numerically.In particular...This study proposes a novel fractional discrete-time macroeconomic system with incommensurate order.The dynamical behavior of the proposed macroeconomic model is investigated analytically and numerically.In particular,the zero equilibrium point stability is investigated to demonstrate that the discrete macroeconomic system exhibits chaotic behavior.Through using bifurcation diagrams,phase attractors,the maximum Lyapunov exponent and the 0–1 test,we verified that chaos exists in the new model with incommensurate fractional orders.Additionally,a complexity analysis is carried out utilizing the approximation entropy(ApEn)and C_(0)complexity to prove that chaos exists.Finally,the main findings of this study are presented using numerical simulations.展开更多
The security of digital images transmitted via the Internet or other public media is of the utmost importance.Image encryption is a method of keeping an image secure while it travels across a non-secure communication ...The security of digital images transmitted via the Internet or other public media is of the utmost importance.Image encryption is a method of keeping an image secure while it travels across a non-secure communication medium where it could be intercepted by unauthorized entities.This study provides an approach to color image encryption that could find practical use in various contexts.The proposed method,which combines four chaotic systems,employs singular value decomposition and a chaotic sequence,making it both secure and compression-friendly.The unified average change intensity,the number of pixels’change rate,information entropy analysis,correlation coefficient analysis,compression friendliness,and security against brute force,statistical analysis and differential attacks are all used to evaluate the algorithm’s performance.Following a thorough investigation of the experimental data,it is concluded that the proposed image encryption approach is secure against a wide range of attacks and provides superior compression friendliness when compared to chaos-based alternatives.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
The advancements in technology have substantially grown the size of image data.Traditional image encryption algorithms have limited capabilities to deal with the emerging challenges in big data,including compression a...The advancements in technology have substantially grown the size of image data.Traditional image encryption algorithms have limited capabilities to deal with the emerging challenges in big data,including compression and noise toleration.An image encryption method that is based on chaotic maps and orthogonal matrix is proposed in this study.The proposed scheme is built on the intriguing characteristics of an orthogonal matrix.Gram Schmidt disperses the values of pixels in a plaintext image by generating a random orthogonal matrix using logistic chaotic map.Following the diffusion process,a block-wise random permutation of the data is performed using multi-chaos.The proposed scheme provides sufficient security and resilience to JPEG compression and channel noise through a series of experiments and security evaluations.It enables Partial Encryption(PE)for faster processing as well as complete encryption for increased security.The higher values of the number of pixels change rates and unified average change intensity confirm the security of the encryption scheme.In contrast to other schemes,the proposed approach can perform full and partial encryption depending on security requirements.展开更多
Cyberattack detection has become an important research domain owing to increasing number of cybercrimes in recent years.Both Machine Learning(ML)and Deep Learning(DL)classification models are useful in effective ident...Cyberattack detection has become an important research domain owing to increasing number of cybercrimes in recent years.Both Machine Learning(ML)and Deep Learning(DL)classification models are useful in effective identification and classification of cyberattacks.In addition,the involvement of hyper parameters in DL models has a significantly influence upon the overall performance of the classification models.In this background,the current study develops Intelligent Cybersecurity Classification using Chaos Game Optimization with Deep Learning(ICC-CGODL)Model.The goal of the proposed ICC-CGODL model is to recognize and categorize different kinds of attacks made upon data.Besides,ICC-CGODL model primarily performs min-max normalization process to normalize the data into uniform format.In addition,Bidirectional Gated Recurrent Unit(BiGRU)model is utilized for detection and classification of cyberattacks.Moreover,CGO algorithm is also exploited to adjust the hyper parameters involved in BiGRU model which is the novelty of current work.A wide-range of simulation analysis was conducted on benchmark dataset and the results obtained confirmed the significant performance of ICC-CGODL technique than the recent approaches.展开更多
In previous works, the theoretical and experimental deterministic scalar kinematic structures, the theoretical and experimental deterministic vector kinematic structures, the theoretical and experimental deterministic...In previous works, the theoretical and experimental deterministic scalar kinematic structures, the theoretical and experimental deterministic vector kinematic structures, the theoretical and experimental deterministic scalar dynamic structures, and the theoretical and experimental deterministic vector dynamic structures have been developed to compute the exact solution for deterministic chaos of the exponential pulsons and oscillons that is governed by the nonstationary three-dimensional Navier-Stokes equations. To explore properties of the kinetic energy, rectangular, diagonal, and triangular summations of a matrix of the kinetic energy and general terms of various sums have been used in the current paper to develop quantization of the kinetic energy of deterministic chaos. Nested structures of a cumulative energy pulson, an energy pulson of propagation, an internal energy oscillon, a diagonal energy oscillon, and an external energy oscillon have been established. In turn, the energy pulsons and oscillons include group pulsons of propagation, internal group oscillons, diagonal group oscillons, and external group oscillons. Sequentially, the group pulsons and oscillons contain wave pulsons of propagation, internal wave oscillons, diagonal wave oscillons, and external wave oscillons. Consecutively, the wave pulsons and oscillons are composed of elementary pulsons of propagation, internal elementary oscillons, diagonal elementary oscillons, and external elementary oscillons. Topology, periodicity, and integral properties of the exponential pulsons and oscillons have been studied using the novel method of the inhomogeneous Fourier expansions via eigenfunctions in coordinates and time. Symbolic computations of the exact expansions have been performed using the experimental and theoretical programming in Maple. Results of the symbolic computations have been justified by probe visualizations.展开更多
An exact three-dimensional solution for stochastic chaos of I wave groups of M random internal waves governed by the Navier-Stokes equations is developed. The Helmholtz decomposition is used to expand the Dirichlet pr...An exact three-dimensional solution for stochastic chaos of I wave groups of M random internal waves governed by the Navier-Stokes equations is developed. The Helmholtz decomposition is used to expand the Dirichlet problem for the Navier-Stokes equations into the Archimedean, Stokes, and Navier problems. The exact solution is obtained with the help of the method of decomposition in invariant structures. Differential algebra is constructed for six families of random invariant structures: random scalar kinematic structures, time-complementary random scalar kinematic structures, random vector kinematic structures, time-complementary random vector kinematic structures, random scalar dynamic structures, and random vector dynamic structures. Tedious computations are performed using the experimental and theoretical programming in Maple. The random scalar and vector kinematic structures and the time-complementary random scalar and vector kinematic structures are applied to solve the Stokes problem. The random scalar and vector dynamic structures are employed to expand scalar and vector variables of the Navier problem. Potentialization of the Navier field becomes available since vortex forces, which are expressed via the vector potentials of the Helmholtz decomposition, counterbalance each other. On the contrary, potential forces, which are described by the scalar potentials of the Helmholtz decomposition, superimpose to generate the gradient of a dynamic random pressure. Various constituents of the kinetic energy are ascribed to diverse interactions of random, three-dimensional, nonlinear, internal waves with a two-fold topology, which are termed random exponential oscillons and pulsons. Quantization of the kinetic energy of stochastic chaos is developed in terms of wave structures of random elementary oscillons, random elementary pulsons, random internal, diagonal, and external elementary oscillons, random wave pulsons, random internal, diagonal, and external wave oscillons, random group pulsons, random internal, diagonal, and external group oscillons, a random energy pulson, random internal, diagonal, and external energy oscillons, and a random cumulative energy pulson.展开更多
In this paper,xve have studied the properties of eigenfunctions in a three-level Lipkin model whose classical counterpart can exhibit classical chaos.In the regime of classical chaotic motions,sensitivity of eigenfunc...In this paper,xve have studied the properties of eigenfunctions in a three-level Lipkin model whose classical counterpart can exhibit classical chaos.In the regime of classical chaotic motions,sensitivity of eigenfunctions to parameter perturbation is exposed,which may be taken as a quantum signature of classical chaos.展开更多
We suggested a method using a small perturbation to modify Lyapunov exponents of the unstable periodic orbit for controlling chaos.The benefit of this control scheme is studied and the effect of noise is discussed.Bas...We suggested a method using a small perturbation to modify Lyapunov exponents of the unstable periodic orbit for controlling chaos.The benefit of this control scheme is studied and the effect of noise is discussed.Based on these studies,a more practical control method is recommended,and some experiments can be better understanded.展开更多
A new experiment on an electric circuit with non-linear ferromagnetic cores is designed to show the roads to chaos.The phase figures of the bifurcations of division of frequency and chaos in the three-dimensional para...A new experiment on an electric circuit with non-linear ferromagnetic cores is designed to show the roads to chaos.The phase figures of the bifurcations of division of frequency and chaos in the three-dimensional parameter space are reported.展开更多
Through replacing Gaussian mutation operator in real-coded genetic algorithm with a chaotic mapping, wepresent a genetic algorithm with chaotic mutation. To examine this new algorithm, we applied our algorithm to func...Through replacing Gaussian mutation operator in real-coded genetic algorithm with a chaotic mapping, wepresent a genetic algorithm with chaotic mutation. To examine this new algorithm, we applied our algorithm to functionoptimization problems and obtained good results. Furthermore the orbital points' distribution of chaotic mapping andthe effects of chaotic mutation with different parameters were studied in order to make the chaotic mutation mechanismbe utilized efficiently.展开更多
Ellipticity as the underlying mechanism for instabilities of physi-cal systems is highlighted in the study of model nonlinear evolution equations withdissipation and the study of phase transition in Van der Waals flui...Ellipticity as the underlying mechanism for instabilities of physi-cal systems is highlighted in the study of model nonlinear evolution equations withdissipation and the study of phase transition in Van der Waals fluid. Interestingresults include spiky solutions, chaotic behavior in the context of partial differentialequations, as well as the nucleation process due to elhpticity in phase transition.展开更多
An improved genetic algorithm (GA) is proposed based on the analysis of population diversity within the framework of Markov chain. The chaos operator to combat premature convergence concerning two goals of maintaining...An improved genetic algorithm (GA) is proposed based on the analysis of population diversity within the framework of Markov chain. The chaos operator to combat premature convergence concerning two goals of maintaining diversity in the population and sustaining the convergence capacity of the GA is introduced. In the CHaos Genetic Algorithm (CHGA), the population is recycled dynamically whereas the most highly fit chromosome is intact so as to restore diversity and reserve the best schemata which may belong to the optimal solution. The characters of chaos as well as advanced operators and parameter settings can improve both exploration and exploitation capacities of the algorithm. The results of multimodal function optimization show that CHGA performs simple genetic algorithms and effectively alleviates the problem of premature convergence.展开更多
The sparrow search algorithm(SSA)is a newly proposed meta-heuristic optimization algorithm based on the sparrowforaging principle.Similar to other meta-heuristic algorithms,SSA has problems such as slowconvergence spe...The sparrow search algorithm(SSA)is a newly proposed meta-heuristic optimization algorithm based on the sparrowforaging principle.Similar to other meta-heuristic algorithms,SSA has problems such as slowconvergence speed and difficulty in jumping out of the local optimum.In order to overcome these shortcomings,a chaotic sparrow search algorithm based on logarithmic spiral strategy and adaptive step strategy(CLSSA)is proposed in this paper.Firstly,in order to balance the exploration and exploitation ability of the algorithm,chaotic mapping is introduced to adjust the main parameters of SSA.Secondly,in order to improve the diversity of the population and enhance the search of the surrounding space,the logarithmic spiral strategy is introduced to improve the sparrow search mechanism.Finally,the adaptive step strategy is introduced to better control the process of algorithm exploitation and exploration.The best chaotic map is determined by different test functions,and the CLSSA with the best chaotic map is applied to solve 23 benchmark functions and 3 classical engineering problems.The simulation results show that the iterative map is the best chaotic map,and CLSSA is efficient and useful for engineering problems,which is better than all comparison algorithms.展开更多
In order to prevent standard genetic algorithm (SGA) from being premature, chaos is introduced into GA,thus forming chaotic anneal genetic algorithm (CAGA). Chaos' ergodicity is used to initialize the population, ...In order to prevent standard genetic algorithm (SGA) from being premature, chaos is introduced into GA,thus forming chaotic anneal genetic algorithm (CAGA). Chaos' ergodicity is used to initialize the population, and chaoticanneal mutation operator is used as the substitute for the mutation operator in SGA. CAGA is a unified framework of theexisting chaotic mutation methods. To validate the proposed algorithm, three algorithms, i.e. Baum-Welch, SGA andCAGA, are compared on training hidden Markov model (HMM) to recognize the hand gestures. Experiments on twenty-six alphabetical gestures show the CAGA's validity.展开更多
In this paper, first, we investigate a novel one-dimensional logistic-PWLCM(LP) modulation map which is derived from the logistic and PWLCM maps. Second, we propose a novel PCLML spatiotemporal chaos in pseudo-random ...In this paper, first, we investigate a novel one-dimensional logistic-PWLCM(LP) modulation map which is derived from the logistic and PWLCM maps. Second, we propose a novel PCLML spatiotemporal chaos in pseudo-random coupling method that can accelerate the system behavior of the fully spatial chaos. Here, because the better chaotic properties include a wide range of parameter settings and better ergodicity than a logistic map, the LP is used in PCLML as f(x). The Kolmogorov–Sinai entropy density and universality and the bifurcation diagram are employed to investigate the chaotic behaviors of the proposed PCLML model. Finally, we apply the LP and PCLML chaotic systems to image encryption to improve the effectiveness and security of the encryption scheme. By combining self-generating matrix model M and dynamic substitution box(S-Box) methods, we design a new image encryption algorithm. Numerical simulations and security analysis have been carried out to demonstrate that the proposed algorithm has a high security level and can efficiently encrypt several different kinds of images into random-like images.展开更多
Chaotic motion and quasi-periodic motion are two common forms of instability in the giant magnetostrictive actuator(GMA).Therefore,in the present study we intend to investigate the influences of the system damping coe...Chaotic motion and quasi-periodic motion are two common forms of instability in the giant magnetostrictive actuator(GMA).Therefore,in the present study we intend to investigate the influences of the system damping coefficient,system stiffness coefficient,disc spring cubic stiffness factor,and the excitation force and frequency on the output stability and the hysteresis vibration of the GMA.In this regard,the nonlinear piezomagnetic equation,Jiles-Atherton hysteresis model,quadratic domain rotation model,and the GMA structural dynamics are used to establish the mathematical model of the hysteresis vibration system of the GMA.Moreover,the multi-scale method and the singularity theory are used to determine the co-dimensional two-bifurcation characteristics of the system.Then,the output response of the system is simulated to determine the variation range of each parameter when chaos is imposed.Finally,the fourth-order Runge-Kutta method is used to obtain the time domain waveform,phase portrait and Poincarémapping diagrams of the system.Subsequently,the obtained three graphs are analyzed.The obtained results show that when the system output is stable,the variation range of each parameter can be determined.Moreover,the stability interval of system damping coefficient,system stiffness coefficient,and the coefficient of the cubic stiffness term of the disc spring are obtained.Furthermore,the stability interval of the exciting force and the excitation frequency are determined.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 61973172, 62003177, 62103204, 62003175, and 61973175)the Joint Fund of the Ministry of Education for Equipment Pre-research (Grant No. 8091B022133)General Terminal IC Interdisciplinary Science Center of Nankai University。
文摘The utilization of thin plate systems based on acoustic vibration holds significant importance in micro-nano manipulation and the exploration of nonlinear science. This paper focuses on the analysis of an actual thin plate system driven by acoustic wave signals. By combining the mechanical analysis of thin plate microelements with the Bubnov–Galerkin integral method, the governing equation for the forced vibration of a square thin plate is derived. Notably,the reaction force of the thin plate vibration system is defined as f=α|w|, resembling Hooke’s law. The energy function and energy level curve of the system are also analyzed. Subsequently, the amplitude–frequency response function of the thin plate oscillator is solved using the harmonic balance method. Through numerical simulations, the amplitude–frequency curves are analyzed for different vibration modes under the influence of various parameters. Furthermore, the paper demonstrates the occurrence of conservative chaotic motions in the thin plate oscillator using theoretical and numerical methods. Dynamics maps illustrating the system’s states are presented to reveal the evolution laws of the system. By exploring the effects of force fields and system energy, the underlying mechanism of chaos is interpreted. Additionally, the phenomenon of chaos in the oscillator can be controlled through the method of velocity and displacement states feedback, which holds significance for engineering applications.
文摘This study proposes a novel fractional discrete-time macroeconomic system with incommensurate order.The dynamical behavior of the proposed macroeconomic model is investigated analytically and numerically.In particular,the zero equilibrium point stability is investigated to demonstrate that the discrete macroeconomic system exhibits chaotic behavior.Through using bifurcation diagrams,phase attractors,the maximum Lyapunov exponent and the 0–1 test,we verified that chaos exists in the new model with incommensurate fractional orders.Additionally,a complexity analysis is carried out utilizing the approximation entropy(ApEn)and C_(0)complexity to prove that chaos exists.Finally,the main findings of this study are presented using numerical simulations.
基金funded by Deanship of Scientific Research at King Khalid University under Grant Number R.G.P.2/86/43.
文摘The security of digital images transmitted via the Internet or other public media is of the utmost importance.Image encryption is a method of keeping an image secure while it travels across a non-secure communication medium where it could be intercepted by unauthorized entities.This study provides an approach to color image encryption that could find practical use in various contexts.The proposed method,which combines four chaotic systems,employs singular value decomposition and a chaotic sequence,making it both secure and compression-friendly.The unified average change intensity,the number of pixels’change rate,information entropy analysis,correlation coefficient analysis,compression friendliness,and security against brute force,statistical analysis and differential attacks are all used to evaluate the algorithm’s performance.Following a thorough investigation of the experimental data,it is concluded that the proposed image encryption approach is secure against a wide range of attacks and provides superior compression friendliness when compared to chaos-based alternatives.
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.
文摘The advancements in technology have substantially grown the size of image data.Traditional image encryption algorithms have limited capabilities to deal with the emerging challenges in big data,including compression and noise toleration.An image encryption method that is based on chaotic maps and orthogonal matrix is proposed in this study.The proposed scheme is built on the intriguing characteristics of an orthogonal matrix.Gram Schmidt disperses the values of pixels in a plaintext image by generating a random orthogonal matrix using logistic chaotic map.Following the diffusion process,a block-wise random permutation of the data is performed using multi-chaos.The proposed scheme provides sufficient security and resilience to JPEG compression and channel noise through a series of experiments and security evaluations.It enables Partial Encryption(PE)for faster processing as well as complete encryption for increased security.The higher values of the number of pixels change rates and unified average change intensity confirm the security of the encryption scheme.In contrast to other schemes,the proposed approach can perform full and partial encryption depending on security requirements.
基金The authors extend their appreciation to the Deanship of Scientific Research at King Khalid University for funding this work under Grant Number(RGP 2/180/43)Princess Nourah bint Abdulrahman University Researchers Supporting Project Number(PNURSP2022R161)+1 种基金Princess Nourah bint Abdulrahman University,Riyadh,Saudi ArabiaThe authors would like to thank the Deanship of Scientific Research at Umm Al-Qura University for supporting this work by Grant Code:(22UQU4210118DSR07).
文摘Cyberattack detection has become an important research domain owing to increasing number of cybercrimes in recent years.Both Machine Learning(ML)and Deep Learning(DL)classification models are useful in effective identification and classification of cyberattacks.In addition,the involvement of hyper parameters in DL models has a significantly influence upon the overall performance of the classification models.In this background,the current study develops Intelligent Cybersecurity Classification using Chaos Game Optimization with Deep Learning(ICC-CGODL)Model.The goal of the proposed ICC-CGODL model is to recognize and categorize different kinds of attacks made upon data.Besides,ICC-CGODL model primarily performs min-max normalization process to normalize the data into uniform format.In addition,Bidirectional Gated Recurrent Unit(BiGRU)model is utilized for detection and classification of cyberattacks.Moreover,CGO algorithm is also exploited to adjust the hyper parameters involved in BiGRU model which is the novelty of current work.A wide-range of simulation analysis was conducted on benchmark dataset and the results obtained confirmed the significant performance of ICC-CGODL technique than the recent approaches.
文摘In previous works, the theoretical and experimental deterministic scalar kinematic structures, the theoretical and experimental deterministic vector kinematic structures, the theoretical and experimental deterministic scalar dynamic structures, and the theoretical and experimental deterministic vector dynamic structures have been developed to compute the exact solution for deterministic chaos of the exponential pulsons and oscillons that is governed by the nonstationary three-dimensional Navier-Stokes equations. To explore properties of the kinetic energy, rectangular, diagonal, and triangular summations of a matrix of the kinetic energy and general terms of various sums have been used in the current paper to develop quantization of the kinetic energy of deterministic chaos. Nested structures of a cumulative energy pulson, an energy pulson of propagation, an internal energy oscillon, a diagonal energy oscillon, and an external energy oscillon have been established. In turn, the energy pulsons and oscillons include group pulsons of propagation, internal group oscillons, diagonal group oscillons, and external group oscillons. Sequentially, the group pulsons and oscillons contain wave pulsons of propagation, internal wave oscillons, diagonal wave oscillons, and external wave oscillons. Consecutively, the wave pulsons and oscillons are composed of elementary pulsons of propagation, internal elementary oscillons, diagonal elementary oscillons, and external elementary oscillons. Topology, periodicity, and integral properties of the exponential pulsons and oscillons have been studied using the novel method of the inhomogeneous Fourier expansions via eigenfunctions in coordinates and time. Symbolic computations of the exact expansions have been performed using the experimental and theoretical programming in Maple. Results of the symbolic computations have been justified by probe visualizations.
文摘An exact three-dimensional solution for stochastic chaos of I wave groups of M random internal waves governed by the Navier-Stokes equations is developed. The Helmholtz decomposition is used to expand the Dirichlet problem for the Navier-Stokes equations into the Archimedean, Stokes, and Navier problems. The exact solution is obtained with the help of the method of decomposition in invariant structures. Differential algebra is constructed for six families of random invariant structures: random scalar kinematic structures, time-complementary random scalar kinematic structures, random vector kinematic structures, time-complementary random vector kinematic structures, random scalar dynamic structures, and random vector dynamic structures. Tedious computations are performed using the experimental and theoretical programming in Maple. The random scalar and vector kinematic structures and the time-complementary random scalar and vector kinematic structures are applied to solve the Stokes problem. The random scalar and vector dynamic structures are employed to expand scalar and vector variables of the Navier problem. Potentialization of the Navier field becomes available since vortex forces, which are expressed via the vector potentials of the Helmholtz decomposition, counterbalance each other. On the contrary, potential forces, which are described by the scalar potentials of the Helmholtz decomposition, superimpose to generate the gradient of a dynamic random pressure. Various constituents of the kinetic energy are ascribed to diverse interactions of random, three-dimensional, nonlinear, internal waves with a two-fold topology, which are termed random exponential oscillons and pulsons. Quantization of the kinetic energy of stochastic chaos is developed in terms of wave structures of random elementary oscillons, random elementary pulsons, random internal, diagonal, and external elementary oscillons, random wave pulsons, random internal, diagonal, and external wave oscillons, random group pulsons, random internal, diagonal, and external group oscillons, a random energy pulson, random internal, diagonal, and external energy oscillons, and a random cumulative energy pulson.
基金Supported by National Basic Research Project"Nonlinear Science"the National Natural Science Foundation of Chinain part by Tianma Foundation of Tianma Microelectronics Co.Ltd.in Shenzhen.
文摘In this paper,xve have studied the properties of eigenfunctions in a three-level Lipkin model whose classical counterpart can exhibit classical chaos.In the regime of classical chaotic motions,sensitivity of eigenfunctions to parameter perturbation is exposed,which may be taken as a quantum signature of classical chaos.
基金Supported by the grand of Chinese National Basic Research Project“Nonlinear Science”the National Natural Science Foundation of China,under Grant No.19175039.
文摘We suggested a method using a small perturbation to modify Lyapunov exponents of the unstable periodic orbit for controlling chaos.The benefit of this control scheme is studied and the effect of noise is discussed.Based on these studies,a more practical control method is recommended,and some experiments can be better understanded.
文摘A new experiment on an electric circuit with non-linear ferromagnetic cores is designed to show the roads to chaos.The phase figures of the bifurcations of division of frequency and chaos in the three-dimensional parameter space are reported.
文摘Through replacing Gaussian mutation operator in real-coded genetic algorithm with a chaotic mapping, wepresent a genetic algorithm with chaotic mutation. To examine this new algorithm, we applied our algorithm to functionoptimization problems and obtained good results. Furthermore the orbital points' distribution of chaotic mapping andthe effects of chaotic mutation with different parameters were studied in order to make the chaotic mutation mechanismbe utilized efficiently.
文摘Ellipticity as the underlying mechanism for instabilities of physi-cal systems is highlighted in the study of model nonlinear evolution equations withdissipation and the study of phase transition in Van der Waals fluid. Interestingresults include spiky solutions, chaotic behavior in the context of partial differentialequations, as well as the nucleation process due to elhpticity in phase transition.
基金The National Natural Science Foundation of China !(No .699740 43 )
文摘An improved genetic algorithm (GA) is proposed based on the analysis of population diversity within the framework of Markov chain. The chaos operator to combat premature convergence concerning two goals of maintaining diversity in the population and sustaining the convergence capacity of the GA is introduced. In the CHaos Genetic Algorithm (CHGA), the population is recycled dynamically whereas the most highly fit chromosome is intact so as to restore diversity and reserve the best schemata which may belong to the optimal solution. The characters of chaos as well as advanced operators and parameter settings can improve both exploration and exploitation capacities of the algorithm. The results of multimodal function optimization show that CHGA performs simple genetic algorithms and effectively alleviates the problem of premature convergence.
基金The Science Foundation of Shanxi Province,China(2020JQ-481,2021JM-224)Aero Science Foundation of China(201951096002).
文摘The sparrow search algorithm(SSA)is a newly proposed meta-heuristic optimization algorithm based on the sparrowforaging principle.Similar to other meta-heuristic algorithms,SSA has problems such as slowconvergence speed and difficulty in jumping out of the local optimum.In order to overcome these shortcomings,a chaotic sparrow search algorithm based on logarithmic spiral strategy and adaptive step strategy(CLSSA)is proposed in this paper.Firstly,in order to balance the exploration and exploitation ability of the algorithm,chaotic mapping is introduced to adjust the main parameters of SSA.Secondly,in order to improve the diversity of the population and enhance the search of the surrounding space,the logarithmic spiral strategy is introduced to improve the sparrow search mechanism.Finally,the adaptive step strategy is introduced to better control the process of algorithm exploitation and exploration.The best chaotic map is determined by different test functions,and the CLSSA with the best chaotic map is applied to solve 23 benchmark functions and 3 classical engineering problems.The simulation results show that the iterative map is the best chaotic map,and CLSSA is efficient and useful for engineering problems,which is better than all comparison algorithms.
文摘In order to prevent standard genetic algorithm (SGA) from being premature, chaos is introduced into GA,thus forming chaotic anneal genetic algorithm (CAGA). Chaos' ergodicity is used to initialize the population, and chaoticanneal mutation operator is used as the substitute for the mutation operator in SGA. CAGA is a unified framework of theexisting chaotic mutation methods. To validate the proposed algorithm, three algorithms, i.e. Baum-Welch, SGA andCAGA, are compared on training hidden Markov model (HMM) to recognize the hand gestures. Experiments on twenty-six alphabetical gestures show the CAGA's validity.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61672124,61370145,and 61173183)the Password Theory Project of the13th Five-Year Plan National Cryptography Development Fund,China(Grant No.MMJJ20170203)+1 种基金the Program for New Century Excellent Talents in Fujian Province Universitythe Natural Science Foundation of Fujian Province of China(Grant No.2018J01100)
文摘In this paper, first, we investigate a novel one-dimensional logistic-PWLCM(LP) modulation map which is derived from the logistic and PWLCM maps. Second, we propose a novel PCLML spatiotemporal chaos in pseudo-random coupling method that can accelerate the system behavior of the fully spatial chaos. Here, because the better chaotic properties include a wide range of parameter settings and better ergodicity than a logistic map, the LP is used in PCLML as f(x). The Kolmogorov–Sinai entropy density and universality and the bifurcation diagram are employed to investigate the chaotic behaviors of the proposed PCLML model. Finally, we apply the LP and PCLML chaotic systems to image encryption to improve the effectiveness and security of the encryption scheme. By combining self-generating matrix model M and dynamic substitution box(S-Box) methods, we design a new image encryption algorithm. Numerical simulations and security analysis have been carried out to demonstrate that the proposed algorithm has a high security level and can efficiently encrypt several different kinds of images into random-like images.
基金Project supported by the Science Fund from the Ministry of Science and Technology of China(Grant No.2017M010660)the Major Project of the Inner Mongolia Autonomous Region,China(Grant No.2018ZD10).
文摘Chaotic motion and quasi-periodic motion are two common forms of instability in the giant magnetostrictive actuator(GMA).Therefore,in the present study we intend to investigate the influences of the system damping coefficient,system stiffness coefficient,disc spring cubic stiffness factor,and the excitation force and frequency on the output stability and the hysteresis vibration of the GMA.In this regard,the nonlinear piezomagnetic equation,Jiles-Atherton hysteresis model,quadratic domain rotation model,and the GMA structural dynamics are used to establish the mathematical model of the hysteresis vibration system of the GMA.Moreover,the multi-scale method and the singularity theory are used to determine the co-dimensional two-bifurcation characteristics of the system.Then,the output response of the system is simulated to determine the variation range of each parameter when chaos is imposed.Finally,the fourth-order Runge-Kutta method is used to obtain the time domain waveform,phase portrait and Poincarémapping diagrams of the system.Subsequently,the obtained three graphs are analyzed.The obtained results show that when the system output is stable,the variation range of each parameter can be determined.Moreover,the stability interval of system damping coefficient,system stiffness coefficient,and the coefficient of the cubic stiffness term of the disc spring are obtained.Furthermore,the stability interval of the exciting force and the excitation frequency are determined.
