Generalized synchronization between two continuous dynamical systems is discussed. By exploring the Liapunov stability theory and constructing appropriately unidirectional coupling term, a sufficient condition for det...Generalized synchronization between two continuous dynamical systems is discussed. By exploring the Liapunov stability theory and constructing appropriately unidirectional coupling term, a sufficient condition for determining the generalized synchronization between continuous systems is proved. Two examples are used to show the effectiveness of this result.展开更多
The approaches for constructing directionally coupled generalized synchronization (GS) systems are presented, which are available for the driving system and the respond system that are in GS via a given diffeomorphi...The approaches for constructing directionally coupled generalized synchronization (GS) systems are presented, which are available for the driving system and the respond system that are in GS via a given diffeomorphism transformation. Examples are proposed for illustrating the methods.展开更多
A more general form of projective synchronization, so called linear generalized synchronization （LGS） is proposed, which includes the generalized projective synchronization （GPS） and the hybrid projective synchron...A more general form of projective synchronization, so called linear generalized synchronization （LGS） is proposed, which includes the generalized projective synchronization （GPS） and the hybrid projective synchronization （HPS） as its special cases, Based on the adaptive technique and Lyapunov stability theory, a general method for achieving the LGS between two chaotic or hyperehaotic systems with uncertain parameters in any scaling matrix is presented. Some numerical simulations are provided to show the effectiveness and feasibility of the proposed synchronization method.展开更多
Based on the Chen chaotic system, a new four-dimensional hyperchaotic Chen system is constructed, and the basic dynamic behaviours of the system were studied, and the generalized synchronization has been observed in t...Based on the Chen chaotic system, a new four-dimensional hyperchaotic Chen system is constructed, and the basic dynamic behaviours of the system were studied, and the generalized synchronization has been observed in the coupled four-dimensional hyperchaotic Chen system with unknown parameters. The Routh Hurwitz theorem is used to derive the conditions of stability of this system. Furthermore based on Lyapunov stability theory, the control laws and adaptive laws of parameters are obtained to make generalized synchronization of the coupled new four-dimensional hyperchaotic Chen systems. Numerical simulation results are presented to illustrate the effectiveness of this method.展开更多
This paper presents a new scheme to achieve generalized synchronization（GS） between different discrete-time chaotic（hyperchaotic） systems.The approach is based on a theorem,which assures that GS is achieved when a...This paper presents a new scheme to achieve generalized synchronization（GS） between different discrete-time chaotic（hyperchaotic） systems.The approach is based on a theorem,which assures that GS is achieved when a structural condition on the considered class of response systems is satisfied.The method presents some useful features：it enables exact GS to be achieved in finite time（i.e.,dead-beat synchronization）;it is rigorous,systematic,and straightforward in checking GS;it can be applied to a wide class of chaotic maps.Some examples of GS,including the Grassi-Miller map and a recently introduced minimal 2-D quadratic map,are illustrated.展开更多
In this paper, with a given manifold y = H（x）, we have constructed a response system for a continuous-time chaotic system as a drive system, and used impulsive control theory to demonstrate theoretically that this r...In this paper, with a given manifold y = H（x）, we have constructed a response system for a continuous-time chaotic system as a drive system, and used impulsive control theory to demonstrate theoretically that this response system can achieve impulsive generalized synchronization （GS） with the drive system. Our theoretical result is supported by numerical examples.展开更多
In this paper, generalized synchronization of two different chaotic dynamical systems is investigated. An active control is adopted to construct a response system which synchronizes with a given drive system for a fun...In this paper, generalized synchronization of two different chaotic dynamical systems is investigated. An active control is adopted to construct a response system which synchronizes with a given drive system for a function relation. Based on rigorous analysis, the error system is asymptotically stable at the equilibrium. Numerical simulations illustrate the effectiveness of the proposed theory.展开更多
This paper introduces the finding of some chaotic attractors in a kind of n-dimensional autonomous hybrid system, which is realized via applying some discontinuous state feedback to a kind of n linear differential sys...This paper introduces the finding of some chaotic attractors in a kind of n-dimensional autonomous hybrid system, which is realized via applying some discontinuous state feedback to a kind of n linear differential system. And a constructive theorem is proposed for generalized synchronization related to the above chaotic hybrid systems. Examples are presented for illustrating the methods.展开更多
The phenomena of GS in a drive-response system have been studied. Several kinds of GS are found： the driver-induced GS, the responser-induced GS, and the intermediate GS. The mechanism generating these types of GS is...The phenomena of GS in a drive-response system have been studied. Several kinds of GS are found： the driver-induced GS, the responser-induced GS, and the intermediate GS. The mechanism generating these types of GS is given and the roles played by response and drive dynamics in realizing different GS states are discussed.展开更多
Based on Lyapunov theory, the adaptive generalized synchronization between Chen system and a multi-scroll chaotic system is investigated. According to the form of target function a proper adaptive controller is design...Based on Lyapunov theory, the adaptive generalized synchronization between Chen system and a multi-scroll chaotic system is investigated. According to the form of target function a proper adaptive controller is designed, by which the controlled Chen system can be synchronized with a multi-scroll chaotic system including unknown parameters. The Lyapunov direct method is exploited to prove that the synchronization error and parameter identification error both converge to zero. Numerical simulation results verify the feasibility of the proposed method further.展开更多
In this paper,using scalar feedback controller and stability theory of fractional-order systems,a gener-alized synchronization method for different fractional-order chaotic systems is established.Simulation results sh...In this paper,using scalar feedback controller and stability theory of fractional-order systems,a gener-alized synchronization method for different fractional-order chaotic systems is established.Simulation results show theeffectiveness of the theoretical results.展开更多
Generalized synchronization of two discrete systems was discussed. By constructing appropriately nonlinear coupling terms, some sufficient conditions for determining the generalized synchronization between the drive a...Generalized synchronization of two discrete systems was discussed. By constructing appropriately nonlinear coupling terms, some sufficient conditions for determining the generalized synchronization between the drive and response systems were derived. In a positive invariant and bounded set, many chaotic maps satisfy the sufficient conditions. The effectiveness of the sufficient conditions is illustrated by three examples.展开更多
The existence of two kinds of generalized synchronization manifold in two unidirectionally coupled discrete stochastic dynamical systems is studied in this paper. When the drive system is chaotic and the modified resp...The existence of two kinds of generalized synchronization manifold in two unidirectionally coupled discrete stochastic dynamical systems is studied in this paper. When the drive system is chaotic and the modified response system collapses to an asymptotically stable equilibrium or asymptotically stable periodic orbit, under certain conditions, the existence of the generalized synchronization can be converted to the problem of a Lipschitz contractive fixed point or Schauder fixed point. Moreover, the exponential attractive property of generalized synchronization manifold is strictly proved. In addition, numerical simulations demonstrate the correctness of the present theory. The physical background and meaning of the results obtained in this paper are also discussed.展开更多
In this paper, a very simple generalized synchronization method between different chaotic systems is presented. Only a scalar controller is used in this method. The method of obtaining the scalar controller from chaot...In this paper, a very simple generalized synchronization method between different chaotic systems is presented. Only a scalar controller is used in this method. The method of obtaining the scalar controller from chaotic systems is established. The sufficient and necessary condition of generalized synchronization is obtained from a rigorous theory, and the sufficient and necessary condition of generalized synchronization is irrelative to chaotic system itself. Theoretical analyses and simulation results show that the method established in this paper is effective.展开更多
Nonlinear dynamics of the time-delayed Mackey-Glass systems is explored. Coexistent multiple chaotic attractors are found. Attractors with double-scroll structures can be well classified in terms of different return t...Nonlinear dynamics of the time-delayed Mackey-Glass systems is explored. Coexistent multiple chaotic attractors are found. Attractors with double-scroll structures can be well classified in terms of different return times within one period of the delay time by constructing the Poincare section. Synchronizations of the drive-response Mackey-Glass oscillators are investigated. The critical coupling strength for the emergence of generalized synchronization against the delay time exhibits the interesting resonant behaviour. We reveal that stronger resonance effect may be observed when different attractors are applied to the drivers, i.e., more resonance peaks can be found.展开更多
In this paper a new dynamic system with integer and fractional order is investigated. It is shown that determining the effect of quadratic coefficients to the systematic structure can be converted to determining that ...In this paper a new dynamic system with integer and fractional order is investigated. It is shown that determining the effect of quadratic coefficients to the systematic structure can be converted to determining that of coefficients of the linear part. Under some parametric conditions, the system can produce chaotic attractors similar as Lorenz attractor. A constructive theorem is proposed for generalized synchronization related to the fractional-order chaotic system and an application of this new system is demonstrated.展开更多
This paper establishes two theorems for two time-delayed （chaotic） discrete systems to achieve timedelayed generalized synchronization （TDGS）. These two theorems uncover the genera/forms of two TDGS systems via a ...This paper establishes two theorems for two time-delayed （chaotic） discrete systems to achieve timedelayed generalized synchronization （TDGS）. These two theorems uncover the genera/forms of two TDGS systems via a prescribed transformation. As examples, we convert the Lorenz three-dimensional chaotic map to an equal time-delayed system as the driving system, and construct the TDGS driven systems according to the Theorems 1 and 2. Numerical simulations demonstrate the effectiveness of the proposed theorems.展开更多
This paper studies the generalized synchronization of a class of drive-response neural networks with time-varying delay. When the topological structures of the drive-response neural networks are known, by designing an...This paper studies the generalized synchronization of a class of drive-response neural networks with time-varying delay. When the topological structures of the drive-response neural networks are known, by designing an appropriate nonlinear adaptive controller, the generalized synchronization of these two networks is obtained based on Lyapunov stability theory and LaSalle’s invariance principle.展开更多
In this paper, a bidirectional partial generalized （lag, complete, and anticipated） synchronization of a class of continuous-time systems is defined. Then based on the active control idea, a new systematic and concr...In this paper, a bidirectional partial generalized （lag, complete, and anticipated） synchronization of a class of continuous-time systems is defined. Then based on the active control idea, a new systematic and concrete scheme is developed to achieve bidirectional partial generalized （lag, complete, and anticipated） synchronization between two chaotic systems or between chaotic and hyperchaotic systems. With the help of symbolic-numerical computation, we choose the modified Chua system, Lorenz system, and the hyperchaotic Tamasevicius Namajunas-Cenys system to illustrate the proposed scheme. Numerical simulations are used to verify the effectiveness of the proposed scheme. It is interesting that partial chaos synchronization not only can take place between two chaotic systems, but also can take place between chaotic and hyperchaotic systems. The proposed scheme can also be extended to research bidirectional partial generalized （lag, complete, and anticipated） synchronization between other dynamical systems.展开更多
This paper is concerned with the existence of adaptive generalized synchronization(GS) of two chaotic systems.An adaptive control is designed based on a Lyapunov approach.By using modified system approach,some suffici...This paper is concerned with the existence of adaptive generalized synchronization(GS) of two chaotic systems.An adaptive control is designed based on a Lyapunov approach.By using modified system approach,some sufficient conditions for the existence of first two types of adaptive GS inertial manifolds are established.Finally,some numerical simulations are provided to illustrate the theoretical results.展开更多
基金Project supported by the National Natural Science Foundation of China(Nos.10672093,10372054 and 70431002)
文摘Generalized synchronization between two continuous dynamical systems is discussed. By exploring the Liapunov stability theory and constructing appropriately unidirectional coupling term, a sufficient condition for determining the generalized synchronization between continuous systems is proved. Two examples are used to show the effectiveness of this result.
文摘The approaches for constructing directionally coupled generalized synchronization (GS) systems are presented, which are available for the driving system and the respond system that are in GS via a given diffeomorphism transformation. Examples are proposed for illustrating the methods.
基金the National Natural Science Foundation of China (60574045 10661006).
文摘A more general form of projective synchronization, so called linear generalized synchronization （LGS） is proposed, which includes the generalized projective synchronization （GPS） and the hybrid projective synchronization （HPS） as its special cases, Based on the adaptive technique and Lyapunov stability theory, a general method for achieving the LGS between two chaotic or hyperehaotic systems with uncertain parameters in any scaling matrix is presented. Some numerical simulations are provided to show the effectiveness and feasibility of the proposed synchronization method.
文摘Based on the Chen chaotic system, a new four-dimensional hyperchaotic Chen system is constructed, and the basic dynamic behaviours of the system were studied, and the generalized synchronization has been observed in the coupled four-dimensional hyperchaotic Chen system with unknown parameters. The Routh Hurwitz theorem is used to derive the conditions of stability of this system. Furthermore based on Lyapunov stability theory, the control laws and adaptive laws of parameters are obtained to make generalized synchronization of the coupled new four-dimensional hyperchaotic Chen systems. Numerical simulation results are presented to illustrate the effectiveness of this method.
文摘This paper presents a new scheme to achieve generalized synchronization（GS） between different discrete-time chaotic（hyperchaotic） systems.The approach is based on a theorem,which assures that GS is achieved when a structural condition on the considered class of response systems is satisfied.The method presents some useful features：it enables exact GS to be achieved in finite time（i.e.,dead-beat synchronization）;it is rigorous,systematic,and straightforward in checking GS;it can be applied to a wide class of chaotic maps.Some examples of GS,including the Grassi-Miller map and a recently introduced minimal 2-D quadratic map,are illustrated.
基金Project supported by the National Natural Science Foundation of China （Grant No 10372054）.
文摘In this paper, with a given manifold y = H（x）, we have constructed a response system for a continuous-time chaotic system as a drive system, and used impulsive control theory to demonstrate theoretically that this response system can achieve impulsive generalized synchronization （GS） with the drive system. Our theoretical result is supported by numerical examples.
文摘In this paper, generalized synchronization of two different chaotic dynamical systems is investigated. An active control is adopted to construct a response system which synchronizes with a given drive system for a function relation. Based on rigorous analysis, the error system is asymptotically stable at the equilibrium. Numerical simulations illustrate the effectiveness of the proposed theory.
基金The project supported by National Natural Science Foundation of China under Grant Nos. 60074034 and 70271068
文摘This paper introduces the finding of some chaotic attractors in a kind of n-dimensional autonomous hybrid system, which is realized via applying some discontinuous state feedback to a kind of n linear differential system. And a constructive theorem is proposed for generalized synchronization related to the above chaotic hybrid systems. Examples are presented for illustrating the methods.
基金National Natural Science Foundation of China under Grant No.10405004
文摘The phenomena of GS in a drive-response system have been studied. Several kinds of GS are found： the driver-induced GS, the responser-induced GS, and the intermediate GS. The mechanism generating these types of GS is given and the roles played by response and drive dynamics in realizing different GS states are discussed.
基金Project supported by the National Natural Science Foundation of China (Grant No. 50875259)
文摘Based on Lyapunov theory, the adaptive generalized synchronization between Chen system and a multi-scroll chaotic system is investigated. According to the form of target function a proper adaptive controller is designed, by which the controlled Chen system can be synchronized with a multi-scroll chaotic system including unknown parameters. The Lyapunov direct method is exploited to prove that the synchronization error and parameter identification error both converge to zero. Numerical simulation results verify the feasibility of the proposed method further.
基金the Foundation of Chongqing Education Committee under Grant No.J070502
文摘In this paper,using scalar feedback controller and stability theory of fractional-order systems,a gener-alized synchronization method for different fractional-order chaotic systems is established.Simulation results show theeffectiveness of the theoretical results.
基金Project supported by the National Natural Science Foundation of China (Nos.10372054 and 70431002)
文摘Generalized synchronization of two discrete systems was discussed. By constructing appropriately nonlinear coupling terms, some sufficient conditions for determining the generalized synchronization between the drive and response systems were derived. In a positive invariant and bounded set, many chaotic maps satisfy the sufficient conditions. The effectiveness of the sufficient conditions is illustrated by three examples.
基金Project supported by the National Natural Science Foundation of China (Grant No.11002061)
文摘The existence of two kinds of generalized synchronization manifold in two unidirectionally coupled discrete stochastic dynamical systems is studied in this paper. When the drive system is chaotic and the modified response system collapses to an asymptotically stable equilibrium or asymptotically stable periodic orbit, under certain conditions, the existence of the generalized synchronization can be converted to the problem of a Lipschitz contractive fixed point or Schauder fixed point. Moreover, the exponential attractive property of generalized synchronization manifold is strictly proved. In addition, numerical simulations demonstrate the correctness of the present theory. The physical background and meaning of the results obtained in this paper are also discussed.
文摘In this paper, a very simple generalized synchronization method between different chaotic systems is presented. Only a scalar controller is used in this method. The method of obtaining the scalar controller from chaotic systems is established. The sufficient and necessary condition of generalized synchronization is obtained from a rigorous theory, and the sufficient and necessary condition of generalized synchronization is irrelative to chaotic system itself. Theoretical analyses and simulation results show that the method established in this paper is effective.
基金Project supported in part by the State Key Program of National Natural Science Foundation of China (Grant No 70431002)the National Basic Research Program of China (Grant No 2007CB814800)+3 种基金the Doctorate Foundation of the State Education Ministry of China (Grant No 20060027009)Supports from the Research Grant Council (RGC)the Hong Kong Baptist University Faculty Research Grant (FRG)the Croucher Foundation of Hong Kong are acknowledged
文摘Nonlinear dynamics of the time-delayed Mackey-Glass systems is explored. Coexistent multiple chaotic attractors are found. Attractors with double-scroll structures can be well classified in terms of different return times within one period of the delay time by constructing the Poincare section. Synchronizations of the drive-response Mackey-Glass oscillators are investigated. The critical coupling strength for the emergence of generalized synchronization against the delay time exhibits the interesting resonant behaviour. We reveal that stronger resonance effect may be observed when different attractors are applied to the drivers, i.e., more resonance peaks can be found.
基金Supported by the National Nature Science Foundation of China under Grant No.60674059
文摘In this paper a new dynamic system with integer and fractional order is investigated. It is shown that determining the effect of quadratic coefficients to the systematic structure can be converted to determining that of coefficients of the linear part. Under some parametric conditions, the system can produce chaotic attractors similar as Lorenz attractor. A constructive theorem is proposed for generalized synchronization related to the fractional-order chaotic system and an application of this new system is demonstrated.
基金Supported by the National Natural Science Foundation of China under Grant No. 60674059
文摘This paper establishes two theorems for two time-delayed （chaotic） discrete systems to achieve timedelayed generalized synchronization （TDGS）. These two theorems uncover the genera/forms of two TDGS systems via a prescribed transformation. As examples, we convert the Lorenz three-dimensional chaotic map to an equal time-delayed system as the driving system, and construct the TDGS driven systems according to the Theorems 1 and 2. Numerical simulations demonstrate the effectiveness of the proposed theorems.
文摘This paper studies the generalized synchronization of a class of drive-response neural networks with time-varying delay. When the topological structures of the drive-response neural networks are known, by designing an appropriate nonlinear adaptive controller, the generalized synchronization of these two networks is obtained based on Lyapunov stability theory and LaSalle’s invariance principle.
基金The author thanks the referees for their valuable suggestions and is very grateful to Dr. Yan Zhen-Ya for his enthusiastic guidance and help.
文摘In this paper, a bidirectional partial generalized （lag, complete, and anticipated） synchronization of a class of continuous-time systems is defined. Then based on the active control idea, a new systematic and concrete scheme is developed to achieve bidirectional partial generalized （lag, complete, and anticipated） synchronization between two chaotic systems or between chaotic and hyperchaotic systems. With the help of symbolic-numerical computation, we choose the modified Chua system, Lorenz system, and the hyperchaotic Tamasevicius Namajunas-Cenys system to illustrate the proposed scheme. Numerical simulations are used to verify the effectiveness of the proposed scheme. It is interesting that partial chaos synchronization not only can take place between two chaotic systems, but also can take place between chaotic and hyperchaotic systems. The proposed scheme can also be extended to research bidirectional partial generalized （lag, complete, and anticipated） synchronization between other dynamical systems.
文摘This paper is concerned with the existence of adaptive generalized synchronization(GS) of two chaotic systems.An adaptive control is designed based on a Lyapunov approach.By using modified system approach,some sufficient conditions for the existence of first two types of adaptive GS inertial manifolds are established.Finally,some numerical simulations are provided to illustrate the theoretical results.
