Synchronization in an array of linearly coupled networks with time-varying delay

Wang, Weiwei; Cao, Jinde

doi:10.1016/j.physa.2005.10.047

Cited by 102 publications

(53 citation statements)

References 28 publications

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“…In [7], Wang and Cao considered an array of linearly coupled delayed neural networks with coupling delay as…”

Section: Notations and Preliminariesmentioning

confidence: 99%

“…A sufficient condition was proposed in [6] for global exponential synchronization of coupled connected neural networks with constant delays by using linear matrix inequality techniques, where the connection matrix is not assumed to be symmetric and irreducible. Wang and Cao [7] studied synchronization in arrays of linearly coupled identical connected neural networks with time-varying delay. In addition, Li and Chen [8] investigated local and global robust adaptive synchronization of uncertain dynamical networks via adaptive techniques.…”

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confidence: 99%

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Synchronization in an array of linearly stochastically coupled networks with time delays

Cao

Wang

Sun

2007

Physica A: Statistical Mechanics and its Applications

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210

106

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In this paper, the complete synchronization problem is investigated in an array of linearly stochastically coupled identical networks with time delays. The stochastic coupling term, which can reflect a more realistic dynamical behavior of coupled systems in practice, is introduced to model a coupled system, and the influence from the stochastic noises on the array of coupled delayed neural networks is studied thoroughly. Based on a simple adaptive feedback control scheme and some stochastic analysis techniques, several sufficient conditions are developed to guarantee the synchronization in an array of linearly stochastically coupled neural networks with time delays.Finally, an illustrate example with numerical simulations is exploited to show the effectiveness of the theoretical results.

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“…In [7], Wang and Cao considered an array of linearly coupled delayed neural networks with coupling delay as…”

Section: Notations and Preliminariesmentioning

confidence: 99%

mentioning

confidence: 99%

Synchronization in an array of linearly stochastically coupled networks with time delays

Cao

Wang

Sun

2007

Physica A: Statistical Mechanics and its Applications

Self Cite

210

106

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show abstract

“…It can be seen from (18) , i = 1, 2, ..., p, are arbitrary matrices which are severed to transfer stable elements between the first two terms in the right hand side of (19) The stability analysis result is summarized in the following theorem.…”

Section: Stability Analysismentioning

confidence: 99%

“…This delayed-feedback control approach was extended to adaptive fuzzy framework [15]. In [17]- [19], the synchronization of neural networks subject to time delay was considered.…”

Section: Introductionmentioning

confidence: 99%

Synchronization of Chaotic Systems Using Time-Delayed Fuzzy State-Feedback Controller

Lam

Ling

Lü³

et al. 2008

IEEE Trans. Circuits Syst. I

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Abstract-This paper presents the fuzzy-model-based control approach to synchronize two chaotic systems subject to parameter uncertainties. A fuzzy state-feedback controller using the system state of response chaotic system and the time-delayed system state of drive chaotic system is employed to realize the synchronization. The time delay which complicates the system dynamics makes the analysis difficult. To investigate the system stability and facilitate the design of fuzzy controller, T-S fuzzy models are employed to represent the system dynamics of the chaotic systems. Furthermore, the membership grades of the T-S fuzzy models become uncertain due to the existence of parameter uncertainties which further complicates the system analysis. To ease the stability analysis and produce less conservative analysis result, the membership functions of both T-S fuzzy models and fuzzy controller are considered. Stability conditions are derived using Lyapunov-based approach to aid the design of fuzzy state-feedback controller to synchronize the chaotic systems. Simulation examples are presented to illustrate the merits of the proposed approach.

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“…Most studies have concentrated on the structure properties of various systems such as the Internet, metabolic networks, neural networks [4], food web, email networks, and so on. Whereas research of collective behavior in arrays of coupled nonlinear systems is also an important issue for understanding the essence of complex networks [5][6][7][8][9][10][11][12][13][14]. Complex dynamical networks can exhibit many interesting phenomena, such as spatio-temporal chaos, spiral waves, auto waves, etc.…”

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confidence: 99%

Adaptive synchronization of uncertain dynamical networks with delayed coupling

Cao

2007

Nonlinear Dyn

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121

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We propose a simple scheme for the synchronization of an uncertain complex dynamical network with delayed coupling. Based on the Lyapunov stability theory of functional differential equations, certain controllers can be designed for ensuring the states of uncertain dynamical network with coupling delays to globally asymptotically synchronize by combining the adaptive method and linear feedback with the updated feedback strength. Different update gains η i will lead to different rates toward synchrony, the choice of which depends on the concrete systems and network models. This strategy can be applied to any complex dynamical network (regular, smallworld, scale-free or random). Numerical examples

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Synchronization in an array of linearly coupled networks with time-varying delay

Cited by 102 publications

References 28 publications

Synchronization in an array of linearly stochastically coupled networks with time delays

Synchronization in an array of linearly stochastically coupled networks with time delays

Synchronization of Chaotic Systems Using Time-Delayed Fuzzy State-Feedback Controller

Adaptive synchronization of uncertain dynamical networks with delayed coupling

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