Adaptive Exponential Synchronization for Stochastic Competitive Neural Networks with Time-Varying Leakage Delays and Reaction-Diffusion Terms

Zhiqiang Wang,Rui Xu,Lili Wang

doi:10.1155/2017/6987436

Abstract

We study the exponential synchronization problem for a class of stochastic competitive neural networks with different timescales, as well as spatial diffusion, time-varying leakage delays, and discrete and distributed time-varying delays. By introducing several important inequalities and using Lyapunov functional technique, an adaptive feedback controller is designed to realize the exponential synchronization for the proposed competitive neural networks in terms of p-norm. According to the theoretical results obtained in this paper, the influences of the timescale, external stimulus constants, disposable scaling constants, and controller parameters on synchronization are analyzed. Numerical simulations are presented to show the feasibility of the theoretical results.

Highlights

Neural networks are mathematical models that are inspired by the structure and functional aspects of biological neural networks
Meyer-Baese et al [1] proposed competitive neural networks with different timescales, which describe the dynamics of cortical cognitive maps with unsupervised synaptic modifications
Based on the above discussion, we are concerned with the combined effects of time-varying leakage delays, stochastic perturbation, and spatial diffusion on the synchronization of competitive neural networks with Neumann boundary conditions in terms of p-norm via an adaptive feedback controller to improve the previous results

Summary

Introduction

Neural networks are mathematical models that are inspired by the structure and functional aspects of biological neural networks. The results about the neural networks with constant delays in the leakage term are imperfect. As far as we know, there are few results concerning the synchronization of competitive neural networks with reaction-diffusion term under Neumann boundary conditions. Based on the above discussion, we are concerned with the combined effects of time-varying leakage delays, stochastic perturbation, and spatial diffusion on the synchronization of competitive neural networks with Neumann boundary conditions in terms of p-norm via an adaptive feedback controller to improve the previous results. To this end, we discuss the following neural networks:.

Preliminary

Exponential Synchronization Criterion

Numerical Simulations

Conclusion