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

Abstract

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.

Robust Synchronization of a Class of Coupled Delayed Networks With Multiple Stochastic Disturbances: The Continuous-Time Case

“…[35]. On the other hand, the nonlinear function f (·) satisfying Assumption 1 is said to belong to the sector [X 1 , X 2 ] and, as pointed out in [16], the nonlinear description (8) is more general than the usually used Lipschitz conditions as in [3][4][5].…”

“…[3,5,10,18,24,41]. For example, in [41], the dynamical behavior has been studied for an array of identical differential equations with linear coupling.…”

“…For example, in [41], the dynamical behavior has been studied for an array of identical differential equations with linear coupling. Considering of the delay effects, the authors of [5] and [18] have dealt with the global synchronization problems, respectively, for a coupled delayed neural network and a complex network with coupling delays. Elegant results have been obtained in [5,18] under the assumptions that 1) the outercoupling matrix of the networks is required to be irreducible so as to avoid isolated clusters; and 2) the inner-coupling matrix is restricted to be symmetric.…”

“…Considering of the delay effects, the authors of [5] and [18] have dealt with the global synchronization problems, respectively, for a coupled delayed neural network and a complex network with coupling delays. Elegant results have been obtained in [5,18] under the assumptions that 1) the outercoupling matrix of the networks is required to be irreducible so as to avoid isolated clusters; and 2) the inner-coupling matrix is restricted to be symmetric. Very recently, a great deal of research efforts have been made towards the improvement of the results in [5,18] under milder assumptions [2,4,10].…”

“…Elegant results have been obtained in [5,18] under the assumptions that 1) the outercoupling matrix of the networks is required to be irreducible so as to avoid isolated clusters; and 2) the inner-coupling matrix is restricted to be symmetric. Very recently, a great deal of research efforts have been made towards the improvement of the results in [5,18] under milder assumptions [2,4,10]. In particular, the properties of Kronecker products have been utilized in [3] and some sufficient criteria have been acquired in the form of linear matrix inequalities (LMIs) that can be readily solved.…”