Periodic oscillatory solution in delayed competitive–cooperative neural networks: A decomposition approach

Abstract

In this paper, the problems of exponential convergence and the exponential stability of the periodic solution for a general class of non-autonomous competitive-cooperative neural networks are analyzed via the decomposition approach. The idea is to divide the connection weights into inhibitory or excitatory types and thereby to embed a competitive-cooperative delayed neural network into an augmented cooperative delay system through a symmetric transformation.Some simple necessary and sufficient conditions are derived to ensure the componentwise exponential convergence and the exponential stability of the periodic solution of the considered neural networks. These results generalize and improve the previous works, and they are easy to check and apply in practice.

Almost periodic solutions of recurrent neural networks with continuously distributed delays

“…In general, it is more likely that delays are variable and there are multiple states, even infinite states due to the presence of various parallel pathways. In other words, the entire history affects the current state; so we need to consider the models which introduce time-varying and distributed delays, and such delay terms may be more suitable for practical neural networks (see [9,13,[17][18][19][20]). …”

“…In the past decades, different classes of recurrent neural networks have been extensively studied due to their promising potential for applications in the areas of signal and image processing, associative memories and pattern classification, parallel computation and optimization problems; see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] and references therein.…”

Periodic Solutions for a Class of Nonautonomous Differential System with Impulses and Time-varying Delays

“…Recently the properties of periodic oscillatory solutions and almost periodic solutions are of great interest because one has found that many networks such as human brain are often in periodic oscillatory or even in chaotic state, see, for example, Refs. [5][6][7][8][9] and references cited therein.…”