Global Synchronization of Coupled Delayed Neural Networks and Applications to Chaotic CNN Models

This paper formulates the model and then studies its dynamics of a system of linearly and diffusively coupled identical delayed neural networks (DNNs), which is generalization of delayed Hopfied neural networks (DHNNs) and delayed cellular neural networks (DCNNs). In particularly, a simple yet generic sufficient condition for global synchronization of such coupled DNNs is derived based on the Lyapunov functional methods and Hermitian matrix theory. It is shown that global synchronization of coupled DNNs is ensured by a suitable design of the coupling matrix and the inner linking matrix. Furthermore, the result is applied to some typical chaotic neural networks. Finally, numerical simulations are presented to demonstrate the effectiveness of the approach.

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

[2]  P. Vadakkepat,et al.  Absolute periodicity and absolute stability of delayed neural networks , 2002 .

[3]  H Lu.  Stability criteria for delayed neural networks. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  R. Desimone,et al.  Modulation of Oscillatory Neuronal Synchronization by Selective Visual Attention , 2001, Science.

[5]  E. Niebur,et al.  Growth patterns in the developing brain detected by using continuum mechanical tensor maps , 2022 .

[6]  A Hjelmfelt,et al.  Pattern recognition, chaos, and multiplicity in neural networks of excitable systems. , 1994, Proceedings of the National Academy of Sciences of the United States of America.

[7]  Louis M. Pecora,et al.  Fundamentals of synchronization in chaotic systems, concepts, and applications. , 1997, Chaos.

[8]  Xiao Fan Wang,et al.  Synchronization in scale-free dynamical networks: robustness and fragility , 2001, cond-mat/0105014.

[9]  M. K. Volkov,et al.  Mesons at finite temperature in the NJL model with gluon condensate , 1993 .

[10]  H. Nijmeijer,et al.  Cooperative oscillatory behavior of mutually coupled dynamical systems , 2001 .

[11]  Hongtao Lu.  Chaotic attractors in delayed neural networks , 2002 .

[12]  L. Pecora.  Synchronization conditions and desynchronizing patterns in coupled limit-cycle and chaotic systems , 1998 .

[13]  Guanrong Chen,et al.  From Chaos To Order Methodologies, Perspectives and Applications , 1998 .

[14]  Xiao Fan Wang,et al.  Synchronization in Small-World Dynamical Networks , 2002, Int. J. Bifurc. Chaos.

[15]  G. Rangarajan,et al.  Stability of synchronized chaos in coupled dynamical systems , 2002, nlin/0201037.

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

[17]  S KalashnikovaYu,et al.  軽‐軽中間子と重‐軽中間子におけるQCDストリング , 2001 .

[18]  L. Chua,et al.  Synchronization in an array of linearly coupled dynamical systems , 1995 .

[19]  W. Freeman,et al.  How brains make chaos in order to make sense of the world , 1987, Behavioral and Brain Sciences.

[20]  Jinde Cao.  Periodic oscillation and exponential stability of delayed CNNs , 2000 .

[21]  Guanrong Chen,et al.  Synchronization stability of three chaotic systems with linear coupling , 2002 .

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

[23]  Guanrong Chen,et al.  A simple global synchronization criterion for coupled chaotic systems , 2003 .