Finite-time stochastic outer synchronization between two complex dynamical networks with different topologies

Sun, Yongzheng; Li, Wang; Zhao, Donghua

doi:10.1063/1.4731265

Cited by 69 publications

(29 citation statements)

References 42 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Note e(t) = (e T 1 (t), e T 2 (t), · · · , e T N (t)) T ; by the well-known L -operator given by the Itô formula [15,23]. Computing the time derivative of V (t) along the trajectories of (7) and combining with Assumption 1, we can obtain:…”

Section: Resultsmentioning

confidence: 99%

Finite-Time Synchronization of Chaotic Complex Networks with Stochastic Disturbance

Jian

2014

Entropy

View full text Add to dashboard Cite

This paper is concerned with the problem of finite-time synchronization in complex networks with stochastic noise perturbations. By using a novel finite-time L -operator differential inequality and other inequality techniques, some novel sufficient conditions are obtained to ensure finite-time stochastic synchronization for the complex networks concerned, where the coupling matrix need not be symmetric. The effects of control parameters on synchronization speed and time are also analyzed, and the synchronization time in this paper is shorter than that in the existing literature. The results here are also applicable to both directed and undirected weighted networks without any information of the coupling matrix. Finally, an example with numerical simulations is given to demonstrate the effectiveness of the proposed method.

show abstract

Section: Resultsmentioning

confidence: 99%

Finite-Time Synchronization of Chaotic Complex Networks with Stochastic Disturbance

Jian

2014

Entropy

View full text Add to dashboard Cite

show abstract

“…Sufficient conditions are obtained to ensure finite-time cluster synchronisation for the complex networks with or without time delays. (iii) The time-delay problem is considered on the finite-time synchronisation of this paper, but many references do not consider this problem because of the mathematical difficulties [20,31,32]. It should be noted that our results can be extended to networked control systems without time delays or Markovian jumping parameters.…”

Section: Introductionmentioning

confidence: 97%

Finite‐time cluster synchronisation of Markovian switching complex networks with stochastic perturbations

Cui

Fang

Zhang

et al. 2014

IET Control Theory & Applications

View full text Add to dashboard Cite

In this study, the authors study the finite-time cluster synchronisation problem for a class of Markovian switching complex networks with stochastic noise perturbations. By constructing the suitable stochastic Lyapunov-Krasovskii functional, using finite-time stability theorem, inequality techniques and the properties of Weiner process, sufficient conditions are obtained to ensure finite-time cluster synchronisation for the complex networks with or without time delays. The effects of control parameters on cluster synchronisation speed and time delays are also analysed. Since finite-time cluster synchronisation means the optimality in convergence time and has better robustness and disturbance rejection properties, this study has important theory significance and practical application value. Finally, numerical examples are examined to illustrate the effectiveness of the analytical results. NomenclatureThroughout this paper, R n and R n×m denote, respectively, the n-dimensional Euclidean space and the set of all n × m real matrices. The superscript 'T' denotes the transpose and the notation X ≥ Y (respectively, X > Y ) where X and Y are symmetric matrices, means that X − Y is positive semi-definite (respectively, positive definite); I N is the identity matrix with compatible dimension. · refers to the Euclidean vector norm; the notation A ⊗ B stands for the Kronecker product of matrices A and B. If A is a matrix, λ min (·) denotes the minimum eigenvalue. diag {· · · } stands for a block-diagonal matrix. E[x] means the expectation of the random variable x. Matrices, if their dimensions are not explicitly stated, are assumed to be compatible for algebraic operations.

show abstract

“…[9][10][11], the effect of noise on the synchronization was analyzed. Due to different applications, a wide variety of approaches and controllers in the network synchronization have been proposed, which include the impulsive control [12,13], pinning control [14,15], adaptive coupling schemes [16,17], open-plus-closedloop scheme [18,19] and the finite-time control [20][21][22].…”

Section: Introductionmentioning

confidence: 99%

Theoretical analysis of synchronization in delayed complex dynamical networks with discontinuous coupling

Sun

Liu

et al. 2016

Nonlinear Dyn

Self Cite

View full text Add to dashboard Cite

In this paper, we study the synchronization problem of time-delayed complex networks with discontinuous coupling. Sufficient conditions for the synchronization are obtained based on the stability theory of differential equations. The theoretical results show that the time-delayed networks can achieve synchronization even if the coupling is switched off sometimes. We find analytically that the speed of synchronization is proportional to the on-off rate of the coupling and the algebraic connectivity of networks. Finally, the analytical results are confirmed by numerical simulations.

show abstract

Finite-time stochastic outer synchronization between two complex dynamical networks with different topologies

Cited by 69 publications

References 42 publications

Finite-Time Synchronization of Chaotic Complex Networks with Stochastic Disturbance

Finite-Time Synchronization of Chaotic Complex Networks with Stochastic Disturbance

Finite‐time cluster synchronisation of Markovian switching complex networks with stochastic perturbations

Theoretical analysis of synchronization in delayed complex dynamical networks with discontinuous coupling

Contact Info

Product

Resources

About