Projective synchronization of neural networks with mixed time-varying delays and parameter mismatch

In this paper, the projective synchronization of neural networks with mixed time-varying delays and parameter mismatch is discussed. Due to parameter mismatch and projective factor, complete projective synchronization cannot be achieved. Therefore, a new weak projective synchronization scheme is proposed to ensure that coupled neural networks are in a state of synchronization with an error level. Several criteria are derived and the error level is estimated by applying a generalized Halanay inequality and matrix measure. Finally, a numerical example is given to verify the efficiencies of theoretical results.

[1]  C. A. Desoer,et al.  Nonlinear Systems Analysis , 1978 .

[2]  Charles R. Johnson,et al.  Topics in Matrix Analysis , 1991 .

[3]  Louis M. Pecora,et al.  Synchronizing chaotic circuits , 1991 .

[4]  M. Vidyasagar,et al.  Nonlinear systems analysis (2nd ed.) , 1993 .

[5]  Parlitz,et al.  Generalized synchronization, predictability, and equivalence of unidirectionally coupled dynamical systems. , 1996, Physical review letters.

[6]  J. Kurths,et al.  From Phase to Lag Synchronization in Coupled Chaotic Oscillators , 1997 .

[7]  T. Carroll,et al.  Synchronization and Imposed Bifurcations in the Presence of Large Parameter Mismatch , 1998 .

[8]  Ronnie Mainieri,et al.  Projective Synchronization In Three-Dimensional Chaotic Systems , 1999 .

[9]  K. Gu An integral inequality in the stability problem of time-delay systems , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[10]  Jürgen Kurths,et al.  Synchronization - A Universal Concept in Nonlinear Sciences , 2001, Cambridge Nonlinear Science Series.

[11]  Jinde Cao,et al.  Global asymptotic stability of bi-directional associative memory networks with distributed delays , 2004, Appl. Math. Comput..

[12]  Shigui Ruan,et al.  Dynamics of a two-neuron system with discrete and distributed delays , 2004 .

[13]  Hongyong Zhao,et al.  Existence and global attractivity of almost periodic solution for cellular neural network with distributed delays , 2004, Appl. Math. Comput..

[14]  Chuandong Li,et al.  Chaotic lag synchronization of coupled time-delayed systems and its applications in secure communication , 2004 .

[15]  Hongyong Zhao,et al.  Global asymptotic stability of Hopfield neural network involving distributed delays , 2004, Neural Networks.

[16]  Ned J Corron,et al.  Lag and anticipating synchronization without time-delay coupling. , 2005, Chaos.

[17]  Zidong Wang,et al.  On global asymptotic stability of neural networks with discrete and distributed delays , 2005 .

[18]  Jianping Yan,et al.  Generalized projective synchronization of a unified chaotic system , 2005 .

[19]  Jinde Cao,et al.  Periodic solutions and its exponential stability of reaction–diffusion recurrent neural networks with continuously distributed delays , 2006 .

[20]  Zidong Wang,et al.  Global exponential stability of generalized recurrent neural networks with discrete and distributed delays , 2006, Neural Networks.

[21]  Yurong Liu,et al.  Stochastic stability of uncertain Hopfield neural networks with discrete and distributed delays , 2006 .

[22]  Xiaofeng Li,et al.  Mismatch robustness and security of chaotic optical communications based on injection-locking chaos synchronization , 2006, IEEE Journal of Quantum Electronics.

[23]  Guohui Li,et al.  Generalized projective synchronization of two chaotic systems by using active control , 2006 .

[24]  Yonghui Sun,et al.  Adaptive lag synchronization of unknown chaotic delayed neural networks with noise perturbation , 2007 .

[25]  Jinde Cao,et al.  Adaptive synchronization of a class of chaotic neural networks with known or unknown parameters , 2008 .

[26]  Liping Wen,et al.  Generalized Halanay inequalities for dissipativity of Volterra functional differential equations , 2008 .

[27]  Zhidong Teng,et al.  Adaptive synchronization of neural networks with time-varying delay and distributed delay , 2008 .

[28]  Jinde Cao,et al.  Adaptive Stabilization and Synchronization for Chaotic Lur'e Systems With Time-Varying Delay , 2008, IEEE Transactions on Circuits and Systems I: Regular Papers.

[29]  Jinde Cao,et al.  Exponential synchronization of chaotic neural networks: a matrix measure approach , 2009 .

[30]  Wanyu Liu,et al.  Robust function projective synchronization of a class of uncertain chaotic systems , 2009 .

[31]  Dibakar Ghosh,et al.  Generalized projective synchronization in time-delayed systems: nonlinear observer approach. , 2009, Chaos.

[32]  Jinde Cao,et al.  Generalized synchronization of chaotic systems: an auxiliary system approach via matrix measure. , 2009, Chaos.

[33]  Hongyue Du,et al.  Function projective synchronization in coupled chaotic systems , 2010 .

[34]  Rafael Castro-Linares,et al.  Trajectory tracking for non-holonomic cars: A linear approach to controlled leader-follower formation , 2010, 49th IEEE Conference on Decision and Control (CDC).

[35]  Hongtao Lu,et al.  Generalized projective synchronization between two different general complex dynamical networks with delayed coupling , 2010 .

[36]  Pengcheng Wei,et al.  Weak synchronization of chaotic neural networks with parameter mismatch via periodically intermittent control , 2011 .