In this paper, we apply a simple adaptive feedback control scheme to synchronize two bi-directionally coupled chaotic systems. Based on the invariance principle of differential equations, sufficient conditions for the...In this paper, we apply a simple adaptive feedback control scheme to synchronize two bi-directionally coupled chaotic systems. Based on the invariance principle of differential equations, sufficient conditions for the global asymptotic synchronization between two bi-directionally coupled chaotic systems via an adaptive feedback controller are given. Unlike other control schemes for bi-directionally coupled systems, this scheme is very simple to implement in practice and need not consider coupling terms. As examples, the autonomous hyperchaotic Chen systems and the new nonautonomous 4D systems are illustrated. Numerical simulations show that the proposed method is effective and robust against the effect of weak noise.展开更多
In this paper, based on the invaxiance principle of differential equations, we propose a simple adaptive control method to synchronize the network with coupling of the general form. Comparing with other control approa...In this paper, based on the invaxiance principle of differential equations, we propose a simple adaptive control method to synchronize the network with coupling of the general form. Comparing with other control approaches, this scheme only depends on each node's state output. So we need not to know the concrete network structure and the solutions of the isolate nodes of the network in advance. In order to demonstrate the effectiveness of the method, a special example is provided and numerical simulations are performed. The numerical results show that our control scheme is very effective and robust against the weak noise.展开更多
In this paper, we investigate complete synchronization of double-delayed RSssler systems with uncertain parameters as the master system is in chaotic synchronization. The uncertain parameters can be nonlinearly expres...In this paper, we investigate complete synchronization of double-delayed RSssler systems with uncertain parameters as the master system is in chaotic synchronization. The uncertain parameters can be nonlinearly expressed in the system. The analysis and proof are given by means of the Lyapunov stability theorem. Based on theoretical analysis, some sufficient conditions of complete synchronization are proved. In order to validate the proposed scheme, numerical simulations are performed and the numerical results show that our scheme is very effective.展开更多
Synchronous firing of neurons is thought to be important for information communication in neuronal networks. This paper investigates the complete and phase synchronization in a heterogeneous small-world chaotic Hindma...Synchronous firing of neurons is thought to be important for information communication in neuronal networks. This paper investigates the complete and phase synchronization in a heterogeneous small-world chaotic Hindmarsh Rose neuronal network. The effects of various network parameters on synchronization behaviour are discussed with some biological explanations. Complete synchronization of small-world neuronal networks is studied theoretically by the master stability function method. It is shown that the coupling strength necessary for complete or phase synchronization decreases with the neuron number, the node degree and the connection density are increased. The effect of heterogeneity of neuronal networks is also considered and it is found that the network heterogeneity has an adverse effect on synchrony.展开更多
According to the Lyapunov stability theorem, a new general hybrid projective complete dislocated synchronization scheme with non-derivative and derivative coupling based on parameter identification is proposed under t...According to the Lyapunov stability theorem, a new general hybrid projective complete dislocated synchronization scheme with non-derivative and derivative coupling based on parameter identification is proposed under the framework of drive-response systems. Every state variable of the response system equals the summation of the hybrid drive systems in the previous hybrid synchronization. However, every state variable of the drive system equals the summation of the hybrid response systems while evolving with time in our method. Complete synchronization, hybrid dislocated synchronization, projective synchronization, non-derivative and derivative coupling, and parameter identification are included as its special item. The Lorenz chaotic system, Rssler chaotic system, memristor chaotic oscillator system, and hyperchaotic Lü system are discussed to show the effectiveness of the proposed methods.展开更多
This paper investigates robust unified (lag, anticipated, and complete) synchronization of two coupled chaotic systems, By introducing the concepts of positive definite symmetrical matrix and Riccati inequality and ...This paper investigates robust unified (lag, anticipated, and complete) synchronization of two coupled chaotic systems, By introducing the concepts of positive definite symmetrical matrix and Riccati inequality and the theory of robust stability, several criteria on robust synchronization are established. Extensive numerical simulations are also used to confirm the results.展开更多
On the basis of numerical computation, the conditions of the modes coupling are proposed, and the high-frequency modes are coupled, but the low frequency modes are uncoupled. It is proved that there exist an absorbing...On the basis of numerical computation, the conditions of the modes coupling are proposed, and the high-frequency modes are coupled, but the low frequency modes are uncoupled. It is proved that there exist an absorbing set and a global finite dimensional attractor which is compact and connected in the function space for the high-frequency modes coupled two Ginzburg-Landau equations(MGLE). The trajectory of driver equation may be spatio-temporal chaotic. One associates with MGLE, a truncated form of the equations. The prepared equations persist in long time dynamical behavior of MGLE. MGLE possess the squeezing properties under some conditions. It is proved that the complete spatio-temporal chaotic synchronization for MGLE can occur. Synchronization phenomenon of infinite dimensional dynamical system (IFDDS) is illustrated on the mathematical theory qualitatively. The method is different from Liapunov function methods and approximate linear methods.展开更多
This paper considers the synchronization of two coupled Hindmarsh-Rose neurons by a pacemaker.Based on the stability theory of differential equations,the complete synchronization of this pacemaker neuron model is reac...This paper considers the synchronization of two coupled Hindmarsh-Rose neurons by a pacemaker.Based on the stability theory of differential equations,the complete synchronization of this pacemaker neuron model is reached.Moreover,we also show that pacemaker can enhance or induce synchronization.Numerical simulations are given to illustrate the main results.展开更多
This paper discuses three types of phase synchronization phenomena in extended Kuramoto model. A certain quadratic form is applied to analyze the stability of phase synchronization manifolds without any stability know...This paper discuses three types of phase synchronization phenomena in extended Kuramoto model. A certain quadratic form is applied to analyze the stability of phase synchronization manifolds without any stability knowledge for error systems. Some simple and convenient criteria are obtained for these types of phase synchronization. Also, the effectiveness of the proposed criteria is illustrated successfully by an example.展开更多
The aim of this paper is to provide a sys- tematic review on the framework to analyze dynamics in recurrently connected neural networks with discontinu- ous right-hand sides with a focus on the authors' works in the ...The aim of this paper is to provide a sys- tematic review on the framework to analyze dynamics in recurrently connected neural networks with discontinu- ous right-hand sides with a focus on the authors' works in the past three years. The concept of the Filippov so- lution is employed to define the solution of the neural network systems by transforming them to differential in- clusions. The theory of viability provides a tool to study the existence and uniqueness of the solution and the Lya- punov function (functional) approach is used to investi- gate the global stability and synchronization. More pre- cisely, we prove that the diagonal-dominant conditions guarantee the existence, uniqueness, and stability of a general class of integro-differential equations with (al- most) periodic self-inhibitions, interconnection weights, inputs, and delays. This model is rather general and in- cludes the well-known Hopfield neural networks, Cohen- Grossberg neural networks, and cellular neural networks as special cases. We extend the absolute stability anal- ysis of gradient-like neural network model by relaxing the analytic constraints so that they can be employed to solve optimization problem with non-smooth cost func- tions. Furthermore, we study the global synchronization problem of a class of linearly coupled neural network with discontinuous right-hand sides.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant Nos 10472091, 10502042 and 10332030) and Graduate Starting Seed Fund of Northwestern Polytechnical University (Grant No Z200655).
文摘In this paper, we apply a simple adaptive feedback control scheme to synchronize two bi-directionally coupled chaotic systems. Based on the invariance principle of differential equations, sufficient conditions for the global asymptotic synchronization between two bi-directionally coupled chaotic systems via an adaptive feedback controller are given. Unlike other control schemes for bi-directionally coupled systems, this scheme is very simple to implement in practice and need not consider coupling terms. As examples, the autonomous hyperchaotic Chen systems and the new nonautonomous 4D systems are illustrated. Numerical simulations show that the proposed method is effective and robust against the effect of weak noise.
基金Project supported by the National Natural Science Foundation of China (Grant Nos 10472091, 10502042 and 10332030) Graduate Starting Seed Fund of Northwestern Polytechnical University, China (Grant No Z200655)
文摘In this paper, based on the invaxiance principle of differential equations, we propose a simple adaptive control method to synchronize the network with coupling of the general form. Comparing with other control approaches, this scheme only depends on each node's state output. So we need not to know the concrete network structure and the solutions of the isolate nodes of the network in advance. In order to demonstrate the effectiveness of the method, a special example is provided and numerical simulations are performed. The numerical results show that our control scheme is very effective and robust against the weak noise.
基金Project supported by the National Natural Science Foundation of China (Grant No.10847110)
文摘In this paper, we investigate complete synchronization of double-delayed RSssler systems with uncertain parameters as the master system is in chaotic synchronization. The uncertain parameters can be nonlinearly expressed in the system. The analysis and proof are given by means of the Lyapunov stability theorem. Based on theoretical analysis, some sufficient conditions of complete synchronization are proved. In order to validate the proposed scheme, numerical simulations are performed and the numerical results show that our scheme is very effective.
基金supported by the National Natural Science Foundation of China (Grant No 10872014)
文摘Synchronous firing of neurons is thought to be important for information communication in neuronal networks. This paper investigates the complete and phase synchronization in a heterogeneous small-world chaotic Hindmarsh Rose neuronal network. The effects of various network parameters on synchronization behaviour are discussed with some biological explanations. Complete synchronization of small-world neuronal networks is studied theoretically by the master stability function method. It is shown that the coupling strength necessary for complete or phase synchronization decreases with the neuron number, the node degree and the connection density are increased. The effect of heterogeneity of neuronal networks is also considered and it is found that the network heterogeneity has an adverse effect on synchrony.
基金Project supported by the State Key Program of the National Natural Science Foundation of China (Grant No. 61134012)the National Natural Science Foundation of China (Grant Nos. 11271146 and 61070238)the Science and Technology Program of Wuhan (Grant No. 20130105010117)
文摘According to the Lyapunov stability theorem, a new general hybrid projective complete dislocated synchronization scheme with non-derivative and derivative coupling based on parameter identification is proposed under the framework of drive-response systems. Every state variable of the response system equals the summation of the hybrid drive systems in the previous hybrid synchronization. However, every state variable of the drive system equals the summation of the hybrid response systems while evolving with time in our method. Complete synchronization, hybrid dislocated synchronization, projective synchronization, non-derivative and derivative coupling, and parameter identification are included as its special item. The Lorenz chaotic system, Rssler chaotic system, memristor chaotic oscillator system, and hyperchaotic Lü system are discussed to show the effectiveness of the proposed methods.
基金Project supported by the National Natural Science Foundation of China (Grant No 10372054).
文摘This paper investigates robust unified (lag, anticipated, and complete) synchronization of two coupled chaotic systems, By introducing the concepts of positive definite symmetrical matrix and Riccati inequality and the theory of robust stability, several criteria on robust synchronization are established. Extensive numerical simulations are also used to confirm the results.
基金Project supported by the National Natural Science Foundation of China (No. 10372054)
文摘On the basis of numerical computation, the conditions of the modes coupling are proposed, and the high-frequency modes are coupled, but the low frequency modes are uncoupled. It is proved that there exist an absorbing set and a global finite dimensional attractor which is compact and connected in the function space for the high-frequency modes coupled two Ginzburg-Landau equations(MGLE). The trajectory of driver equation may be spatio-temporal chaotic. One associates with MGLE, a truncated form of the equations. The prepared equations persist in long time dynamical behavior of MGLE. MGLE possess the squeezing properties under some conditions. It is proved that the complete spatio-temporal chaotic synchronization for MGLE can occur. Synchronization phenomenon of infinite dimensional dynamical system (IFDDS) is illustrated on the mathematical theory qualitatively. The method is different from Liapunov function methods and approximate linear methods.
基金supported by the National Natural Science Foundation of China (1087201410802012)
文摘This paper considers the synchronization of two coupled Hindmarsh-Rose neurons by a pacemaker.Based on the stability theory of differential equations,the complete synchronization of this pacemaker neuron model is reached.Moreover,we also show that pacemaker can enhance or induce synchronization.Numerical simulations are given to illustrate the main results.
文摘This paper discuses three types of phase synchronization phenomena in extended Kuramoto model. A certain quadratic form is applied to analyze the stability of phase synchronization manifolds without any stability knowledge for error systems. Some simple and convenient criteria are obtained for these types of phase synchronization. Also, the effectiveness of the proposed criteria is illustrated successfully by an example.
文摘The aim of this paper is to provide a sys- tematic review on the framework to analyze dynamics in recurrently connected neural networks with discontinu- ous right-hand sides with a focus on the authors' works in the past three years. The concept of the Filippov so- lution is employed to define the solution of the neural network systems by transforming them to differential in- clusions. The theory of viability provides a tool to study the existence and uniqueness of the solution and the Lya- punov function (functional) approach is used to investi- gate the global stability and synchronization. More pre- cisely, we prove that the diagonal-dominant conditions guarantee the existence, uniqueness, and stability of a general class of integro-differential equations with (al- most) periodic self-inhibitions, interconnection weights, inputs, and delays. This model is rather general and in- cludes the well-known Hopfield neural networks, Cohen- Grossberg neural networks, and cellular neural networks as special cases. We extend the absolute stability anal- ysis of gradient-like neural network model by relaxing the analytic constraints so that they can be employed to solve optimization problem with non-smooth cost func- tions. Furthermore, we study the global synchronization problem of a class of linearly coupled neural network with discontinuous right-hand sides.