Unified synchronization criteria in an array of coupled neural networks with hybrid impulses

This paper investigates the problem of globally exponential synchronization of coupled neural networks with hybrid impulses. Two new concepts on average impulsive interval and average impulsive gain are proposed to deal with the difficulties coming from hybrid impulses. By employing the Lyapunov method combined with some mathematical analysis, some efficient unified criteria are obtained to guarantee the globally exponential synchronization of impulsive networks. Our method and criteria are proved to be effective for impulsively coupled neural networks simultaneously with synchronizing impulses and desynchronizing impulses, and we do not need to discuss these two kinds of impulses separately. Moreover, by using our average impulsive interval method, we can obtain an interesting and valuable result for the case of average impulsive interval Ta=∞. For some sparse impulsive sequences with Ta=∞, the impulses can happen for infinite number of times, but they do not have essential influence on the synchronization property of networks. Finally, numerical examples including scale-free networks are exploited to illustrate our theoretical results.

[1]  Zhenjiang Zhao,et al.  Global exponential stability of impulsive complex-valued neural networks with both asynchronous time-varying and continuously distributed delays , 2016, Neural Networks.

[2]  Vadim N. Biktashev,et al.  Autowave principles for parallel image processing , 1991 .

[3]  Jinde Cao,et al.  Multiagent Systems on Multilayer Networks: Synchronization Analysis and Network Design , 2017, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[4]  Ligang Wu,et al.  Exponential stabilization of switched stochastic dynamical networks , 2009 .

[5]  Yong Xu,et al.  State Estimation for Periodic Neural Networks With Uncertain Weight Matrices and Markovian Jump Channel States , 2018, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[6]  Yuxia Li,et al.  Stability and Hopf Bifurcation of Fractional-Order Complex-Valued Single Neuron Model with Time Delay , 2017, Int. J. Bifurc. Chaos.

[7]  Fuad E. Alsaadi,et al.  Synchronization of Heterogeneous Partially Coupled Networks with Heterogeneous Impulses , 2017, Neural Processing Letters.

[8]  Chuandong Li,et al.  Robust stability of stochastic fuzzy delayed neural networks with impulsive time window , 2015, Neural Networks.

[9]  Chai Wah Wu,et al.  Synchronization in Complex Networks of Nonlinear Dynamical Systems , 2008 .

[10]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[11]  Jia Jia,et al.  Quasi-synchronisation of fractional-order memristor-based neural networks with parameter mismatches , 2017 .

[12]  Jinde Cao,et al.  Pinning cluster synchronization in an array of coupled neural networks under event-based mechanism , 2016, Neural Networks.

[13]  T. Carroll,et al.  Master Stability Functions for Synchronized Coupled Systems , 1998 .

[14]  Tao Yang,et al.  Impulsive Systems and Control: Theory and Applications , 2001 .

[15]  Qian Ma,et al.  Finite-time synchronization for complex dynamical networks with time-varying delays , 2012 .

[16]  Renquan Lu,et al.  Asynchronous Dissipative State Estimation for Stochastic Complex Networks With Quantized Jumping Coupling and Uncertain Measurements , 2017, IEEE Transactions on Neural Networks and Learning Systems.

[17]  Jurgen Kurths,et al.  Synchronization in complex networks , 2008, 0805.2976.

[18]  Tianping Chen,et al.  New approach to synchronization analysis of linearly coupled ordinary differential systems , 2006 .

[19]  Daniel W. C. Ho,et al.  Globally Exponential Synchronization and Synchronizability for General Dynamical Networks , 2010, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[20]  Zhenjiang Zhao,et al.  Global exponential stability of complex-valued neural networks with both time-varying delays and impulsive effects , 2016, Neural Networks.

[21]  Jinde Cao,et al.  Pinning-controlled synchronization of delayed neural networks with distributed-delay coupling via impulsive control , 2017, Neural Networks.

[22]  Yuanyuan Li,et al.  Impulsive Synchronization of Stochastic Neural Networks via Controlling Partial States , 2017, Neural Processing Letters.

[23]  Fan Chung,et al.  Spectral Graph Theory , 1996 .

[24]  Jinde Cao,et al.  Aperiodically intermittent control for synchronization of switched complex networks with unstable modes via matrix $$\varvec{\omega }$$ω-measure approach , 2018 .

[25]  Frank C. Hoppensteadt,et al.  Pattern recognition via synchronization in phase-locked loop neural networks , 2000, IEEE Trans. Neural Networks Learn. Syst..

[26]  Zhen Wang,et al.  Reduced-order observer design for the synchronization of the generalized Lorenz chaotic systems , 2012, Appl. Math. Comput..

[27]  Jinde Cao,et al.  Pth Moment Exponential Stochastic Synchronization of Coupled Memristor-based Neural Networks with Mixed Delays via Delayed Impulsive Control , 2015, Neural Networks.

[28]  Tingwen Huang,et al.  Controllability and Synchronization Analysis of Identical-Hierarchy Mixed-Valued Logical Control Networks , 2017, IEEE Transactions on Cybernetics.

[29]  Wai Keung Wong,et al.  Stochastic Synchronization of Complex Networks With Mixed Impulses , 2013, IEEE Transactions on Circuits and Systems I: Regular Papers.

[30]  Jinde Cao,et al.  Synchronization Control for Nonlinear Stochastic Dynamical Networks: Pinning Impulsive Strategy , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[31]  Jing Wang,et al.  synchronization for singularly perturbed complex networks with semi-Markov jump topology , 2018, Appl. Math. Comput..

[32]  Xinzhi Liu,et al.  Robust impulsive synchronization of uncertain dynamical networks , 2005, IEEE Transactions on Circuits and Systems I: Regular Papers.

[33]  D. Ho,et al.  Stabilization of complex dynamical networks with noise disturbance under performance constraint , 2011 .

[34]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[35]  Jinde Cao,et al.  Outer synchronization of partially coupled dynamical networks via pinning impulsive controllers , 2015, J. Frankl. Inst..

[36]  Jinde Cao,et al.  Pinning impulsive stabilization of nonlinear Dynamical Networks with Time-Varying Delay , 2012, Int. J. Bifurc. Chaos.

[37]  Gang Feng,et al.  Reliable dissipative control for stochastic impulsive systems , 2008, Autom..

[38]  Feng Qian,et al.  Network-based leader-following consensus of nonlinear multi-agent systems via distributed impulsive control , 2017, Inf. Sci..

[39]  Daniel W. C. Ho,et al.  Pinning Stabilization of Linearly Coupled Stochastic Neural Networks via Minimum Number of Controllers , 2009, IEEE Transactions on Neural Networks.

[40]  F. Zou,et al.  Bifurcation and chaos in cellular neural networks , 1993 .

[41]  Xiaodi Li,et al.  Stabilization of Delay Systems: Delay-Dependent Impulsive Control , 2017, IEEE Transactions on Automatic Control.

[42]  Xiaodi Li,et al.  Stability of nonlinear differential systems with state-dependent delayed impulses , 2016, Autom..

[43]  Jinde Cao,et al.  A unified synchronization criterion for impulsive dynamical networks , 2010, Autom..

[44]  James Lam,et al.  Quasi-synchronization of heterogeneous dynamic networks via distributed impulsive control: Error estimation, optimization and design , 2015, Autom..

[45]  Xin Wang,et al.  Impulsive exponential synchronization of randomly coupled neural networks with Markovian jumping and mixed model-dependent time delays , 2014, Neural Networks.

[46]  Daniel W. C. Ho,et al.  Finite-Time Cluster Synchronization of T–S Fuzzy Complex Networks With Discontinuous Subsystems and Random Coupling Delays , 2015, IEEE Transactions on Fuzzy Systems.

[47]  Tonghua Zhang,et al.  Dynamics analysis and numerical simulations of a stochastic non-autonomous predator–prey system with impulsive effects , 2017 .