Research on synchronization of chaotic delayed neural networks with stochastic perturbation using impulsive control method

Abstract In this paper, an impulsive controller is designed to achieve the exponential synchronization of chaotic delayed neural networks with stochastic perturbation. By using the impulsive delay differential inequality technique that was established in recent publications, several sufficient conditions ensuring the exponential synchronization of chaotic delayed networks are derived, which can be easily checked by LMI Control Toolbox in Matlab. A numerical example and its simulation is given to demonstrate the effectiveness and advantage of the theory results.

[1]  Mohammad Haeri,et al.  Modified impulsive synchronization of hyperchaotic systems , 2010 .

[2]  Ju H. Park Synchronization of cellular neural networks of neutral type via dynamic feedback controller , 2009 .

[3]  Parlitz,et al.  Driving and synchronizing by chaotic impulses. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[4]  Xiaodi Li,et al.  Synchronization of chaotic delayed neural networks with impulsive and stochastic perturbations , 2011 .

[5]  Xiaodi Li,et al.  New results on global exponential stabilization of impulsive functional differential equations with infinite delays or finite delays , 2010 .

[6]  D. Baĭnov,et al.  Systems with impulse effect : stability, theory, and applications , 1989 .

[7]  Alexander O. Ignatyev,et al.  On the stability of invariant sets of systems with impulse effect , 2008 .

[8]  Xinzhi Liu,et al.  Stability of impulsive control systems with time delay , 2004 .

[9]  Yang Tao,et al.  Impulsive stabilization for control and synchronization of chaotic systems: theory and application to secure communication , 1997 .

[10]  Allan R. Willms,et al.  Impulsive controllability of linear dynamical systems with applications to maneuvers of spacecraft , 1996 .

[11]  Changming Ding,et al.  Synchronization of stochastic perturbed chaotic neural networks with mixed delays , 2010, J. Frankl. Inst..

[12]  Xinzhi Liu,et al.  Impulsive synchronization of chaotic systems subject to time delay , 2009 .

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

[14]  Jinde Cao,et al.  Robust impulsive synchronization of coupled delayed neural networks with uncertainties , 2007 .

[15]  Zijiang Yang,et al.  Lag Synchronization of Unknown Chaotic Delayed Yang–Yang-Type Fuzzy Neural Networks With Noise Perturbation Based on Adaptive Control and Parameter Identification , 2009, IEEE Transactions on Neural Networks.

[16]  John E. Prussing,et al.  Optimal Impulsive Time-Fixed Direct-Ascent Interception , 1989 .

[17]  Xinzhi Liu,et al.  Application of Impulsive Synchronization to Communication Security , 2003 .

[18]  J. Liang,et al.  Robust Synchronization of an Array of Coupled Stochastic Discrete-Time Delayed Neural Networks , 2008, IEEE Transactions on Neural Networks.

[19]  V. Lakshmikantham,et al.  Theory of Impulsive Differential Equations , 1989, Series in Modern Applied Mathematics.

[20]  Jianhua Shen,et al.  Impulsive stabilization of functional differential equations by Lyapunov-Razumikhin functions , 1999 .

[21]  A. A. Soliman,et al.  Asymptotic stability and instability of the solutions of systems with impulse action , 2006 .

[22]  Maoan Han,et al.  Synchronization schemes for coupled identical Yang–Yang type fuzzy cellular neural networks , 2009 .

[23]  Qidi Wu,et al.  Impulsive control for the stabilization and synchronization of Lorenz systems , 2002 .

[24]  Jinde Cao,et al.  Adaptive synchronization of neural networks with or without time-varying delay. , 2006, Chaos.

[25]  Jinde Cao,et al.  Exponential synchronization of stochastic perturbed chaotic delayed neural networks , 2007, Neurocomputing.

[26]  Xiaodi Li,et al.  Existence and global exponential stability of periodic solution for impulsive Cohen-Grossberg-type BAM neural networks with continuously distributed delays , 2009, Appl. Math. Comput..

[27]  M. Gilli Strange attractors in delayed cellular neural networks , 1993 .

[28]  R. Rakkiyappan,et al.  Impulsive controller design for exponential synchronization of chaotic neural networks with mixed delays , 2013, Commun. Nonlinear Sci. Numer. Simul..

[29]  Qiankun Song,et al.  Design of controller on synchronization of chaotic neural networks with mixed time-varying delays , 2009, Neurocomputing.

[30]  Xiaodi Li,et al.  Lag synchronization of chaotic delayed neural networks via impulsive control , 2012, IMA Journal of Mathematical Control and Information.

[31]  Patricia J. Y. Wong,et al.  Global exponential stability of a class of retarded impulsive differential equations with applications , 2009 .

[32]  Qiankun Song,et al.  Synchronization analysis of coupled connected neural networks with mixed time delays , 2009, Neurocomputing.

[33]  L. Chua,et al.  Impulsive control and synchronization of nonlinear dynamical systems and application to secure communication , 1997 .

[34]  Katrin Rohlf,et al.  Impulsive control of a Lotka-Volterra system , 1998 .

[35]  Martin Bohner,et al.  An impulsive delay differential inequality and applications , 2012, Comput. Math. Appl..

[36]  S. Mohammed Stochastic functional differential equations , 1984 .

[37]  Jinde Cao,et al.  Global Asymptotical Stability of Recurrent Neural Networks With Multiple Discrete Delays and Distributed Delays , 2006, IEEE Transactions on Neural Networks.

[38]  Jitao Sun,et al.  Robust synchronization of coupled delayed neural networks under general impulsive control , 2009 .