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Complete synchronization between two bi-directionally coupled chaotic systems via an adaptive feedback controller 被引量:4
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作者 肖玉柱 徐伟 《Chinese Physics B》 SCIE EI CAS CSCD 2007年第6期1597-1602,共6页
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
关键词 complete synchronization bi-directionally coupled systems adaptive control
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Complete synchronization of uncertain chaotic dynamical network via a simple adaptive control 被引量:3
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作者 肖玉柱 徐伟 +1 位作者 李秀春 唐素芳 《Chinese Physics B》 SCIE EI CAS CSCD 2008年第1期80-86,共7页
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
关键词 complete synchronization adaptive control dynamical network
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Complete synchronization of double-delayed Rssler systems with uncertain parameters
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作者 桑金玉 杨吉 岳立娟 《Chinese Physics B》 SCIE EI CAS CSCD 2011年第8期120-124,共5页
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
关键词 complete synchronization double-delayed Rossler system uncertain parameters
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Complete and phase synchronization in a heterogeneous small-world neuronal network 被引量:5
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作者 韩芳 陆启韶 +1 位作者 Wiercigroch Marian 季全宝 《Chinese Physics B》 SCIE EI CAS CSCD 2009年第2期482-488,共7页
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
关键词 small-world neuronal network complete synchronization phase synchronization het erogeneity
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General hybrid projective complete dislocated synchronization with non-derivative and derivative coupling based on parameter identification in several chaotic and hyperchaotic systems
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作者 孙军伟 沈轶 +2 位作者 张国东 王延峰 崔光照 《Chinese Physics B》 SCIE EI CAS CSCD 2013年第4期185-195,共11页
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
关键词 complete dislocated synchronization parameter identification non-derivative and derivative coupling memristor chaotic oscillator system
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Robust synchronization of uncertain chaotic systems 被引量:2
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作者 李芳 胡爱花 徐振源 《Chinese Physics B》 SCIE EI CAS CSCD 2006年第3期507-512,共6页
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
关键词 robust unified synchronization complete synchronization lag synchronization anticipated synchronization
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SPATIO-TEMPORAL CHAOTIC SYNCHRONIZATION FOR MODES COUPLED TWO GINZBURG-LANDAU EQUATIONS
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作者 胡满峰 徐振源 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2006年第8期1149-1156,共8页
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
关键词 complete synchronization Ginzberg-Landau equations ATTRACTOR spatiotemporal chaos
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Synchronization in Complex Networks with Multiple Connections
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作者 吴庆初 傅新楚 孙伟刚 《Communications in Theoretical Physics》 SCIE CAS CSCD 2010年第1期200-204,共5页
In this paper a class of networks with multiple connections are discussed. The multiple connections include two different types of links between nodes in complex networks. For this new model, we give a simple generati... In this paper a class of networks with multiple connections are discussed. The multiple connections include two different types of links between nodes in complex networks. For this new model, we give a simple generating procedure. Furthermore, we investigate dynamical synchronization behavior in a delayed two-layer network, giving corresponding theoretical analysis and numerical examples. 展开更多
关键词 complete synchronization two-layer network delayed feedback
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Synchronization in Oscillator Networks with Nonlinear Coupling
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作者 ZHANG Jian-Bao LIU Zeng-Rong LI Ying 《Communications in Theoretical Physics》 SCIE CAS CSCD 2008年第10期925-930,共6页
Synchronization in coupled oscillator networks has attracted much attention from many fields of science and engineering. In this paper, it is firstly proved that the oscifiator network with nonlinear coupling is also ... Synchronization in coupled oscillator networks has attracted much attention from many fields of science and engineering. In this paper, it is firstly proved that the oscifiator network with nonlinear coupling is also eventually dissipative under the hypothesis of eventual dissipation of the uncoupled oscillators. And the dynamics of the network is analyzed in its absorbing domain by combining two methods developed recently. Suufficient conditions for synchronization in the oscillator networks with nonlinear coupling are obtained. The two methods are combined effectively and the results embody the respective merits of the two methods. Numerical simulations confirm the validity of the results. 展开更多
关键词 complete synchronization nonlinear coupling Lyapunov function approach
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Suppression of Noises in Open-Loop-Closed-Loop Coupled Systems
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作者 徐培 付传技 邬劭轶 《Communications in Theoretical Physics》 SCIE CAS CSCD 2010年第6期1100-1104,共5页
Suppression of noises is studied for the open-loop-closed-loop (OPCL) coupling systems between the driver and response systems. In OPCL coupling systems, the error signal of noise is found to be suppressed and shows... Suppression of noises is studied for the open-loop-closed-loop (OPCL) coupling systems between the driver and response systems. In OPCL coupling systems, the error signal of noise is found to be suppressed and shows bounds. The error signal can be decreased exponentially by enlarging the absolute value of the eigenvalues' real part of the Hurwitz matrix. A method is provided to reduce the error signal sufficiently and achieve complete synchronization (US) effectively for the OPCL coupling systems under noises. Based on this method, three numerical examples are reported in this paper, 展开更多
关键词 OPCL coupling systems upper bound complete synchronization Hurwitz matrix
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SYNCHRONIZATION OF TWO COUPLED HINDMARSH-ROSE NEURONS BY A PACEMAKER
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作者 Meisheng Li (School of Math.and Systems Science,Beihang University,Beijing 100191) Honghui Zhang (Dept.of Dynamics and Control,Beihang University,Beijing 100191) Yong Zhao (College of Math.and Information Sci.,Henan Polytechnic University,Jiaozuo 454000,Henan) 《Annals of Differential Equations》 2011年第4期454-459,共6页
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
关键词 Floquet multiplier PACEMAKER complete synchronization
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A RESEARCH ON PHASE SYNCHRONIZATION FOR EXTENDED KURAMOTO MODEL
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作者 Jianhua Xu Changling Han 《Annals of Differential Equations》 2014年第2期216-221,共6页
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
关键词 extended Kuramoto model clustering phase synchronization frequency synchronization complete phase synchronization asymptotically stability
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Dynamical behaviors of recurrently connected neural networks and linearly coupled networks with discontinuous right-hand sides
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作者 Wenlian LU Tianping CHEN +1 位作者 Bo LIU Xiangnan HE 《Frontiers of Electrical and Electronic Engineering in China》 CSCD 2012年第1期32-48,共17页
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
关键词 delayed integro-differential system discontinuous activation ahnost periodic function nonsmooth cost function complete synchronization
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