Synchronization in Arrays of Delay-Coupled Neural Networks via Adaptive Control

In this paper, we firstly proposed a general complex dynamical network consisting of N nonlinearly coupled identical neural networks with coupling delays. Many studied coupled systems are special cases of this model. Synchronization in such dynamical network is studied. By using the Lyapunov stability theorem, some simple controllers with updated feedback strength are introduced in to make the network synchronized. The update gain Upsii can be properly chosen to make some important nodes synchronized quicker or slower than other nodes. One example is given to verify the validity and effectiveness of the proposed control scheme.

[1]  Guanrong Chen,et al.  Complex networks: small-world, scale-free and beyond , 2003 .

[2]  S. Strogatz.  Exploring complex networks , 2001, Nature.

[3]  Junan Lu,et al.  Adaptive synchronization of an uncertain complex dynamical network , 2006, IEEE Transactions on Automatic Control.

[4]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[5]  Jinde Cao,et al.  Adaptive synchronization in tree-like dynamical networks , 2007 .

[6]  Vicente Pérez-Muñuzuri,et al.  Autowaves for Image Processing on a Two-Dimensional CNN Array of Excitable Nonlinear Circuits: Flat and Wrinkled Labyrinths V. Perez-Mufiuzuri, V. Perez-Villar, and Leon 0. Chua, Fellow, ZEEE , 1993 .

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

[8]  Jinde Cao,et al.  Global synchronization in arrays of delayed neural networks with constant and delayed coupling , 2006 .

[9]  Chunguang Li,et al.  Synchronization in general complex dynamical networks with coupling delays , 2004 .

[10]  Jinde Cao,et al.  Topology influences performance in the associative memory neural networks , 2006 .

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

[12]  Donghua Zhou,et al.  Synchronization in uncertain complex networks. , 2006, Chaos.

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

[14]  V. P ez-Villar,et al.  Autowaves for Image Processing on a Two-Dimensional CNN Array of Excitable Nonlinear Circuits: Flat and Wrinkled Labyrinths V. Perez-Mufiuzuri, V. Perez-Villar, and Leon 0. Chua, Fellow, ZEEE , 1993 .

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

[16]  Jinde Cao,et al.  A general framework for global asymptotic stability analysis of delayed neural networks based on LMI approach , 2005 .

[17]  Guanrong Chen,et al.  Global Synchronization of Coupled Delayed Neural Networks and Applications to Chaotic CNN Models , 2004, Int. J. Bifurc. Chaos.

[18]  Xiang Li,et al.  Pinning a complex dynamical network to its equilibrium , 2004, IEEE Trans. Circuits Syst. I Regul. Pap..

[19]  Shengyuan Xu,et al.  Novel global asymptotic stability criteria for delayed cellular neural networks , 2005, IEEE Transactions on Circuits and Systems II: Express Briefs.

[20]  J J Hopfield,et al.  Neurons with graded response have collective computational properties like those of two-state neurons. , 1984, Proceedings of the National Academy of Sciences of the United States of America.

[21]  Xiao Fan Wang,et al.  Complex Networks: Topology, Dynamics and Synchronization , 2002, Int. J. Bifurc. Chaos.

[22]  Debin Huang,et al.  A Simple Adaptive-feedback Controller for Identical Chaos Synchronization , 2022 .

[23]  Ramakrishna Ramaswamy,et al.  TARGETING CHAOS THROUGH ADAPTIVE CONTROL , 1998, chao-dyn/9801024.

[24]  Tianping Chen,et al.  Synchronization of coupled connected neural networks with delays , 2004, IEEE Transactions on Circuits and Systems I: Regular Papers.