In this paper,the problem of combination projection synchronization of fractional-order complex dynamic networks with time-varying delay couplings and external interferences is studied.Firstly,the definition of combin...In this paper,the problem of combination projection synchronization of fractional-order complex dynamic networks with time-varying delay couplings and external interferences is studied.Firstly,the definition of combination projection synchronization of fractional-order complex dynamic networks is given,and the synchronization problem of the drive-response systems is transformed into the stability problem of the error system.In addition,time-varying delays and disturbances are taken into consideration to make the network synchronization more practical and universal.Then,based on Lyapunov stability theory and fractional inequality theory,the adaptive controller is formulated to make the drive and response systems synchronization by the scaling factors.The controller is easier to realize because there is no time-delay term in the controller.At last,the corresponding simulation examples demonstrate the effectiveness of the proposed scheme.展开更多
Projective synchronization problems of a drive system and a particular response network were investigated,where the drive system is an arbitrary system with n+1 dimensions;it may be a linear or nonlinear system,and ev...Projective synchronization problems of a drive system and a particular response network were investigated,where the drive system is an arbitrary system with n+1 dimensions;it may be a linear or nonlinear system,and even a chaotic or hyperchaotic system,the response network is complex system coupled by N nodes,and every node is showed by the approximately linear part of the drive system.Only controlling any one node of the response network by designed controller can achieve the projective synchronization.Some numerical examples were employed to verify the effectiveness and correctness of the designed controller.展开更多
Synchronization of fractional-order chaotic systems is receiving significant attention in the literature due to its applications in a variety of fields,including cryptography,optics,and secure communications.In this p...Synchronization of fractional-order chaotic systems is receiving significant attention in the literature due to its applications in a variety of fields,including cryptography,optics,and secure communications.In this paper,a three-dimensional fractional-order chaotic Lorenz model of chemical reactions is discussed.Some basic dynamical properties,such as stability of equilibria,Lyapunov exponents,bifurcation diagrams,Poincarémap,and sensitivity to initial conditions,are studied.By adopting the Adomian decomposition algorithm(ADM),the numerical solution of the fractional-order system is obtained.It is found that the lowest derivative order in which the proposed system exhibits chaos is q=0.694 by applying ADM.The result has been validated by the existence of one positive Lyapunov exponent and by employing some phase diagrams.In addition,the richer dynamics of the system are confirmed by using powerful tools in nonlinear dynamic analysis,such as the 0-1 test and C_(0)complexity.Moreover,modified projective synchronization has been implemented based on the stability theory of fractional-order systems.This paper presents the application of the modified projective synchronization in secure communication,where the information signal can be transmitted and recovered successfully through the channel.MATLAB simulations are provided to show the validity of the constructed secure communication scheme.展开更多
In this paper is investigated the generalized projective synchronization of a class of chaotic （or hyperchaotic） systems, in which certain parameters can be separated from uncertain parameters. Based on the adaptive...In this paper is investigated the generalized projective synchronization of a class of chaotic （or hyperchaotic） systems, in which certain parameters can be separated from uncertain parameters. Based on the adaptive technique, the globally generalized projective synchronization of two identical chaotic （hyperchaotic） systems is achieved by designing a novel nonlinear controller. Furthermore, the parameter identification is realized simultaneously. A sufficient condition for the globally projective synchronization is obtained. Finally, by taking the hyperchaotic L system as example, some numerical simulations are provided to demonstrate the effectiveness and feasibility of the proposed technique.展开更多
This study addresses the adaptive control and function projective synchronization problems between 2D Rulkov discrete-time system and Network discrete-time system. Based on backstepping design with three controllers, ...This study addresses the adaptive control and function projective synchronization problems between 2D Rulkov discrete-time system and Network discrete-time system. Based on backstepping design with three controllers, a systematic, concrete and automatic scheme is developed to investigate the function projective synchronization of discretetime chaotic systems. In addition, the adaptive control function is applied to achieve the state synchronization of two discrete-time systems. Numerical results demonstrate the effectiveness of the proposed control scheme.展开更多
This paper proposes a method to achieve projective synchronization of the fractional order chaotic Rossler system. First, construct the fractional order Rossler system＇s corresponding approximate integer order system...This paper proposes a method to achieve projective synchronization of the fractional order chaotic Rossler system. First, construct the fractional order Rossler system＇s corresponding approximate integer order system, then a control method based on a partially linear decomposition and negative feedback of state errors is utilized on the new integer order system. Mathematic analyses prove the feasibility and the numerical simulations show the effectiveness of the proposed method.展开更多
Projective synchronization and generalized projective synchronization have recently been observed in the coupled chaotic systems. In this paper, a new synchronization, called ＂generalized projective synchronization＂...Projective synchronization and generalized projective synchronization have recently been observed in the coupled chaotic systems. In this paper, a new synchronization, called ＂generalized projective synchronization＂, is reported in the chaotic Lorenz system and the chaotic Chen one.展开更多
A function projective synchronization of two identical hyperchaotic systems is defined and the theorem of sufficient condition is given. Based on the active control method and symbolic computation Maple, the scheme of...A function projective synchronization of two identical hyperchaotic systems is defined and the theorem of sufficient condition is given. Based on the active control method and symbolic computation Maple, the scheme of function projective synchronization is developed to synchronize the two identical new hyperchaotic systems constructed by Yan up to a scaling function matrix with different initial values. Numerical simulations are used to verify the effectiveness of the scheme.展开更多
In this paper, a new method for controlling projective synchronization in coupled chaotic systems is presented. The control method is based on a partially linear decomposition and negative feedback of state errors. Fi...In this paper, a new method for controlling projective synchronization in coupled chaotic systems is presented. The control method is based on a partially linear decomposition and negative feedback of state errors. Firstly, the synchronizability of the proposed projective synchronization control method is proved mathematically. Then, three different representative examples are discussed to verify the correctness and effectiveness of the proposed control method.展开更多
Based on fractional-order Lyapunov stability theory, this paper provides a novel method to achieve robust modified projective synchronization of two uncertain fractional-order chaotic systems with external disturbance...Based on fractional-order Lyapunov stability theory, this paper provides a novel method to achieve robust modified projective synchronization of two uncertain fractional-order chaotic systems with external disturbance. Simulation of the fractional-order Lorenz chaotic system and fractional-order Chen＇s chaotic system with both parameters uncertainty and external disturbance show the applicability and the efficiency of the proposed scheme.展开更多
Based on the stability theory of the linear fractional order system, projective synchronization of a complex network is studied in the paper, and the coupling functions of the connected nodes are identified. With this...Based on the stability theory of the linear fractional order system, projective synchronization of a complex network is studied in the paper, and the coupling functions of the connected nodes are identified. With this method, the projective synchronization of the network with different fractional order chaos nodes can be achieved, besides, the number of the nodes does not affect the stability of the whole network. In the numerical simulations, the chaotic fractional order Lu system, Liu system and Coullet system are chosen as examples to show the effectiveness of the scheme.展开更多
In this paper, the modified projective synchronization （MPS） of a fractional-order hyperchaotic system is inves- tigated. We design the response system corresponding to the drive system on the basis of projective sy...In this paper, the modified projective synchronization （MPS） of a fractional-order hyperchaotic system is inves- tigated. We design the response system corresponding to the drive system on the basis of projective synchronization theory, and determine the sufficient condition for the synchronization of the drive system and the response system based on fractional-order stability theory. The MPS of a fractional-order hyperchaotic system is achieved by transmitting a single variable. This scheme reduces the information transmission in order to achieve the synchronization, and extends the applicable scope of MPS. Numerical simulations further demonstrate the feasibility and the effectiveness of the proposed scheme.展开更多
In this paper, a simple adaptive linear feedback control method is proposed for controlling the scaling factor between two coupled unified chaotic systems to a desired value, based on the invarianee principle of diffe...In this paper, a simple adaptive linear feedback control method is proposed for controlling the scaling factor between two coupled unified chaotic systems to a desired value, based on the invarianee principle of differential equations. Under this control strategy, one can arbitrarily select the scaling factor. Numerical simulations are given to support the effectiveness of the proposed method and show the robustness against noise. Furthermore, a secure communication scheme based on the adaptive projective synchronization of unified chaotic systems is presented and numerical simulation shows its feasibility.展开更多
We further study the projective synchronization of a new hyperchaotic system. Different from the most existing methods, intermittent control is applied to chaotic synchronization in the present paper. We formulate the...We further study the projective synchronization of a new hyperchaotic system. Different from the most existing methods, intermittent control is applied to chaotic synchronization in the present paper. We formulate the intermittent control system that governs the dynamics of the projective synchronization error, then derive the sufficient conditions for the exponential stability of intermittent control system by using the Lyapunov stability theory, and finally establish the periodically intermittent controller according to the stability criterion by which the projective synchronization is expected to be achieved. The analytical results are also demonstrated by several numerical simulations.展开更多
The adaptive generalized matrix projective lag synchronization between two different complex networks with non-identical nodes and different dimensions is investigated in this paper. Based on Lyapunov stability theory...The adaptive generalized matrix projective lag synchronization between two different complex networks with non-identical nodes and different dimensions is investigated in this paper. Based on Lyapunov stability theory and Barbalat＇s lemma, generalized matrix projective lag synchronization criteria are derived by using the adaptive control method. Furthermore, each network can be undirected or directed, connected or disconnected, and nodes in either network may have identical or different dynamics. The proposed strategy is applicable to almost all kinds of complex networks. In addition, numerical simulation results are presented to illustrate the effectiveness of this method, showing that the synchronization speed is sensitively influenced by the adaptive law strength, the network size, and the network topological structure.展开更多
Function projective lag synchronization of different structural fractional-order chaotic systems is investigated. It is shown that the slave system can be synchronized with the past states of the driver up to a scalin...Function projective lag synchronization of different structural fractional-order chaotic systems is investigated. It is shown that the slave system can be synchronized with the past states of the driver up to a scaling function matrix. According to the stability theorem of linear fractional-order systems, a nonlinear fractional-order controller is designed for the synchronization of systems with the same and different dimensions. Especially, for two different dimensional systems, the synchronization is achieved in both reduced and increased dimensions. Three kinds of numerical examples are presented to illustrate the effectiveness of the scheme.展开更多
This paper investigates the projective synchronization and lag synchronization of a new hyperchaotic system[Physica A 364(2006)103].On the basis of Lyapunov stability theory,two novel nonlinear controllers are respect...This paper investigates the projective synchronization and lag synchronization of a new hyperchaotic system[Physica A 364(2006)103].On the basis of Lyapunov stability theory,two novel nonlinear controllers are respectivelydesigned to guarantee the global exponential projective synchronization(including complete synchronization and anti-synchronization)and lag synchronization.Finally,numerical simulations are given to show the effectiveness of the mainresults.展开更多
An adaptive fuzzy sliding mode strategy is developed for the generalized projective synchronization of a fractional- order chaotic system, where the slave system is not necessarily known in advance. Based on the desig...An adaptive fuzzy sliding mode strategy is developed for the generalized projective synchronization of a fractional- order chaotic system, where the slave system is not necessarily known in advance. Based on the designed adaptive update laws and the linear feedback method, the adaptive fuzzy sliding controllers are proposed via the fuzzy design, and the strength of the designed controllers can he adaptively adjusted according to the external disturbances. Based on the Lya- punov stability theorem, the stability and the robustness of the controlled system are proved theoretically. Numerical simu- lations further support the theoretical results of the paper and demonstrate the efficiency of the proposed method. Moreover, it is revealed that the proposed method allows us to manipulate arbitrarily the response dynamics of the slave system by adjusting the desired scaling factor λi and the desired translating factor ηi, which may be used in a channel-independent chaotic secure communication.展开更多
In this paper, the hybrid function projective synchronization (HFPS) of different chaotic systems with uncertain periodically time-varying parameters is carried out by Fourier series expansion and adaptive bounding te...In this paper, the hybrid function projective synchronization (HFPS) of different chaotic systems with uncertain periodically time-varying parameters is carried out by Fourier series expansion and adaptive bounding technique. Fourier series expansion is used to deal with uncertain periodically time-varying parameters. Adaptive bounding technique is used to compensate the bound of truncation errors. Using the Lyapunov stability theory, an adaptive control law and six parameter updating laws are constructed to make the states of two different chaotic systems asymptotically synchronized. The control strategy does not need to know the parameters thoroughly if the time-varying parameters are periodical functions. Finally, in order to verify the effectiveness of the proposed scheme, the HFPS between Lorenz system and Chen system is completed successfully by using this scheme.展开更多
We study different types of projective synchronization （projective-anticipating, projective, and projectivelag synchronization） in a class of time-delayed chaotic systems related to optical bistable or hybrid optica...We study different types of projective synchronization （projective-anticipating, projective, and projectivelag synchronization） in a class of time-delayed chaotic systems related to optical bistable or hybrid optical bistable devices. We relax some limitations of previous work, where the scaling factor a can not be any desired value. In this paper, we achieve projective-anticipating, projective, and projective-lag synchronization without the limitation of a. A suitable controller is chosen using active control approach. Based on the Lyapunov stability theory, we derive the sufficient stability condition through theoretical analysis. The analytical results are validated by the numerical simulations using Ikeda model and Mackey-Glass model.展开更多
基金supported in part by the National Natural Science Foundation of China(Grant no.61775198,62076222,61903342)Henan Province Science and technology research project(Grant no.222102210059,222102210266,212102310455)。
文摘In this paper,the problem of combination projection synchronization of fractional-order complex dynamic networks with time-varying delay couplings and external interferences is studied.Firstly,the definition of combination projection synchronization of fractional-order complex dynamic networks is given,and the synchronization problem of the drive-response systems is transformed into the stability problem of the error system.In addition,time-varying delays and disturbances are taken into consideration to make the network synchronization more practical and universal.Then,based on Lyapunov stability theory and fractional inequality theory,the adaptive controller is formulated to make the drive and response systems synchronization by the scaling factors.The controller is easier to realize because there is no time-delay term in the controller.At last,the corresponding simulation examples demonstrate the effectiveness of the proposed scheme.
基金Supported by the National Natural Science Foundation of China (11161027)。
文摘Projective synchronization problems of a drive system and a particular response network were investigated,where the drive system is an arbitrary system with n+1 dimensions;it may be a linear or nonlinear system,and even a chaotic or hyperchaotic system,the response network is complex system coupled by N nodes,and every node is showed by the approximately linear part of the drive system.Only controlling any one node of the response network by designed controller can achieve the projective synchronization.Some numerical examples were employed to verify the effectiveness and correctness of the designed controller.
文摘Synchronization of fractional-order chaotic systems is receiving significant attention in the literature due to its applications in a variety of fields,including cryptography,optics,and secure communications.In this paper,a three-dimensional fractional-order chaotic Lorenz model of chemical reactions is discussed.Some basic dynamical properties,such as stability of equilibria,Lyapunov exponents,bifurcation diagrams,Poincarémap,and sensitivity to initial conditions,are studied.By adopting the Adomian decomposition algorithm(ADM),the numerical solution of the fractional-order system is obtained.It is found that the lowest derivative order in which the proposed system exhibits chaos is q=0.694 by applying ADM.The result has been validated by the existence of one positive Lyapunov exponent and by employing some phase diagrams.In addition,the richer dynamics of the system are confirmed by using powerful tools in nonlinear dynamic analysis,such as the 0-1 test and C_(0)complexity.Moreover,modified projective synchronization has been implemented based on the stability theory of fractional-order systems.This paper presents the application of the modified projective synchronization in secure communication,where the information signal can be transmitted and recovered successfully through the channel.MATLAB simulations are provided to show the validity of the constructed secure communication scheme.
基金Project supported by the National Natural Science Foundation of China （Grant No 60574045） and partly by Foundation of Guangxi Department of Education, China （Grant No （2006）26-118）.
文摘In this paper is investigated the generalized projective synchronization of a class of chaotic （or hyperchaotic） systems, in which certain parameters can be separated from uncertain parameters. Based on the adaptive technique, the globally generalized projective synchronization of two identical chaotic （hyperchaotic） systems is achieved by designing a novel nonlinear controller. Furthermore, the parameter identification is realized simultaneously. A sufficient condition for the globally projective synchronization is obtained. Finally, by taking the hyperchaotic L system as example, some numerical simulations are provided to demonstrate the effectiveness and feasibility of the proposed technique.
基金supported by the Natural Science Foundation of China under Grant Nos.10747141 and 10735030Zhejiang Provincial Natural Science Foundation under Grant No.605408+3 种基金Ningbo Natural Science Foundation under Grant Nos.2007A610049 and 2008A61001National Basic Research Program of China (973 Program 2007CB814800)Programme for Changjiang Scholars and Innovative Research Team in University (IRT0734)K.C.Wong Magna Fund in Ningbo University
文摘This study addresses the adaptive control and function projective synchronization problems between 2D Rulkov discrete-time system and Network discrete-time system. Based on backstepping design with three controllers, a systematic, concrete and automatic scheme is developed to investigate the function projective synchronization of discretetime chaotic systems. In addition, the adaptive control function is applied to achieve the state synchronization of two discrete-time systems. Numerical results demonstrate the effectiveness of the proposed control scheme.
基金Project supported by the Key Youth Project of Southwest University for Nationalities of China and the Natural Science Foundation of the State Nationalities Affairs Commission of China （Grant Nos 05XN07 and 07XN05）.
文摘This paper proposes a method to achieve projective synchronization of the fractional order chaotic Rossler system. First, construct the fractional order Rossler system＇s corresponding approximate integer order system, then a control method based on a partially linear decomposition and negative feedback of state errors is utilized on the new integer order system. Mathematic analyses prove the feasibility and the numerical simulations show the effectiveness of the proposed method.
基金Project supported by Tianyuan Foundation of China （ Grant No. A0324651）, and Natural Science Foundation of Hunaa Province of China （Grant No. 03JJY3014）
文摘Projective synchronization and generalized projective synchronization have recently been observed in the coupled chaotic systems. In this paper, a new synchronization, called ＂generalized projective synchronization＂, is reported in the chaotic Lorenz system and the chaotic Chen one.
基金＊The project supported by the Natural Science Foundations of Zhejiang Province under Grant No. Y604056 and the Doctoral Foundation of Ningbo City under Grant No. 2005A61030
文摘A function projective synchronization of two identical hyperchaotic systems is defined and the theorem of sufficient condition is given. Based on the active control method and symbolic computation Maple, the scheme of function projective synchronization is developed to synchronize the two identical new hyperchaotic systems constructed by Yan up to a scaling function matrix with different initial values. Numerical simulations are used to verify the effectiveness of the scheme.
基金Project supported by the National Nature Science Foundation of China （Grant No 70571017）.
文摘In this paper, a new method for controlling projective synchronization in coupled chaotic systems is presented. The control method is based on a partially linear decomposition and negative feedback of state errors. Firstly, the synchronizability of the proposed projective synchronization control method is proved mathematically. Then, three different representative examples are discussed to verify the correctness and effectiveness of the proposed control method.
基金Project supported by the National Natural Science Foundation of China(Grant No.61203041)the Fundamental Research Funds for the Central Universities of China(Grant No.11MG49)
文摘Based on fractional-order Lyapunov stability theory, this paper provides a novel method to achieve robust modified projective synchronization of two uncertain fractional-order chaotic systems with external disturbance. Simulation of the fractional-order Lorenz chaotic system and fractional-order Chen＇s chaotic system with both parameters uncertainty and external disturbance show the applicability and the efficiency of the proposed scheme.
基金Project supported by the National Natural Science Foundation of China(Nos.60573172and60973152)the Superior University Doctor Subject Special Scientific Research Foundation of China(Grant No.20070141014)the Natural Science Foundation of Liaoning Province,China(Grant No.20082165)
文摘Based on the stability theory of the linear fractional order system, projective synchronization of a complex network is studied in the paper, and the coupling functions of the connected nodes are identified. With this method, the projective synchronization of the network with different fractional order chaos nodes can be achieved, besides, the number of the nodes does not affect the stability of the whole network. In the numerical simulations, the chaotic fractional order Lu system, Liu system and Coullet system are chosen as examples to show the effectiveness of the scheme.
基金supported by the National Natural Science Foundation of China (Grant Nos. 60573172 and 60973152)the Superior University Doctor Subject Special Scientific Research Foundation of China (Grant No. 20070141014)the Natural Science Foundation of Liaoning Province, China (Grant No. 20082165)
文摘In this paper, the modified projective synchronization （MPS） of a fractional-order hyperchaotic system is inves- tigated. We design the response system corresponding to the drive system on the basis of projective synchronization theory, and determine the sufficient condition for the synchronization of the drive system and the response system based on fractional-order stability theory. The MPS of a fractional-order hyperchaotic system is achieved by transmitting a single variable. This scheme reduces the information transmission in order to achieve the synchronization, and extends the applicable scope of MPS. Numerical simulations further demonstrate the feasibility and the effectiveness of the proposed scheme.
基金Project supported in part by the National Natural Science Foundation of China （Grant Nos 10372054 and 60575038） and the Science Foundation of Southern Yangtze University of China （Grant No 000408）.
文摘In this paper, a simple adaptive linear feedback control method is proposed for controlling the scaling factor between two coupled unified chaotic systems to a desired value, based on the invarianee principle of differential equations. Under this control strategy, one can arbitrarily select the scaling factor. Numerical simulations are given to support the effectiveness of the proposed method and show the robustness against noise. Furthermore, a secure communication scheme based on the adaptive projective synchronization of unified chaotic systems is presented and numerical simulation shows its feasibility.
基金Project supported by the National Natural Science Foundation of China (Grant No. 60974020)the Natural Science Foundation of Chongqing, China (Grant No. cstc2011jjA0980)the Foundation of Chongqing Education College, China (Grant Nos. KY201112A, KY201113B, and KY201122C )
文摘We further study the projective synchronization of a new hyperchaotic system. Different from the most existing methods, intermittent control is applied to chaotic synchronization in the present paper. We formulate the intermittent control system that governs the dynamics of the projective synchronization error, then derive the sufficient conditions for the exponential stability of intermittent control system by using the Lyapunov stability theory, and finally establish the periodically intermittent controller according to the stability criterion by which the projective synchronization is expected to be achieved. The analytical results are also demonstrated by several numerical simulations.
文摘The adaptive generalized matrix projective lag synchronization between two different complex networks with non-identical nodes and different dimensions is investigated in this paper. Based on Lyapunov stability theory and Barbalat＇s lemma, generalized matrix projective lag synchronization criteria are derived by using the adaptive control method. Furthermore, each network can be undirected or directed, connected or disconnected, and nodes in either network may have identical or different dynamics. The proposed strategy is applicable to almost all kinds of complex networks. In addition, numerical simulation results are presented to illustrate the effectiveness of this method, showing that the synchronization speed is sensitively influenced by the adaptive law strength, the network size, and the network topological structure.
基金Project supported by the National Natural Science Foundation of China(Grant No.11371049)the Science Foundation of Beijing Jiaotong University(Grant Nos.2011JBM130 and 2011YJS076)
文摘Function projective lag synchronization of different structural fractional-order chaotic systems is investigated. It is shown that the slave system can be synchronized with the past states of the driver up to a scaling function matrix. According to the stability theorem of linear fractional-order systems, a nonlinear fractional-order controller is designed for the synchronization of systems with the same and different dimensions. Especially, for two different dimensional systems, the synchronization is achieved in both reduced and increased dimensions. Three kinds of numerical examples are presented to illustrate the effectiveness of the scheme.
基金supported by the National Natural Science Foundation of China under Grant No. 60574045
文摘This paper investigates the projective synchronization and lag synchronization of a new hyperchaotic system[Physica A 364(2006)103].On the basis of Lyapunov stability theory,two novel nonlinear controllers are respectivelydesigned to guarantee the global exponential projective synchronization(including complete synchronization and anti-synchronization)and lag synchronization.Finally,numerical simulations are given to show the effectiveness of the mainresults.
基金Project supported by the Research Foundation of Education Bureau of Hebei Province,China(Grant No.QN2014096)
文摘An adaptive fuzzy sliding mode strategy is developed for the generalized projective synchronization of a fractional- order chaotic system, where the slave system is not necessarily known in advance. Based on the designed adaptive update laws and the linear feedback method, the adaptive fuzzy sliding controllers are proposed via the fuzzy design, and the strength of the designed controllers can he adaptively adjusted according to the external disturbances. Based on the Lya- punov stability theorem, the stability and the robustness of the controlled system are proved theoretically. Numerical simu- lations further support the theoretical results of the paper and demonstrate the efficiency of the proposed method. Moreover, it is revealed that the proposed method allows us to manipulate arbitrarily the response dynamics of the slave system by adjusting the desired scaling factor λi and the desired translating factor ηi, which may be used in a channel-independent chaotic secure communication.
基金supported by National Natural Science Foundation of China (No.60974139)Fundamental Research Funds for the Central Universities (No.72103676)
文摘In this paper, the hybrid function projective synchronization (HFPS) of different chaotic systems with uncertain periodically time-varying parameters is carried out by Fourier series expansion and adaptive bounding technique. Fourier series expansion is used to deal with uncertain periodically time-varying parameters. Adaptive bounding technique is used to compensate the bound of truncation errors. Using the Lyapunov stability theory, an adaptive control law and six parameter updating laws are constructed to make the states of two different chaotic systems asymptotically synchronized. The control strategy does not need to know the parameters thoroughly if the time-varying parameters are periodical functions. Finally, in order to verify the effectiveness of the proposed scheme, the HFPS between Lorenz system and Chen system is completed successfully by using this scheme.
基金Supported by Research Project of Hubei Provincial Department of Education under Grant No.Q20101609Foundation of Wuhan Textile University under Grant No.105040
文摘We study different types of projective synchronization （projective-anticipating, projective, and projectivelag synchronization） in a class of time-delayed chaotic systems related to optical bistable or hybrid optical bistable devices. We relax some limitations of previous work, where the scaling factor a can not be any desired value. In this paper, we achieve projective-anticipating, projective, and projective-lag synchronization without the limitation of a. A suitable controller is chosen using active control approach. Based on the Lyapunov stability theory, we derive the sufficient stability condition through theoretical analysis. The analytical results are validated by the numerical simulations using Ikeda model and Mackey-Glass model.
