Global robust exponential synchronization of BAM recurrent FNNs with infinite distributed delays and diffusion terms on time scales

Kaihong Zhao

doi:10.1186/1687-1847-2014-317

Abstract

In this article, the global robust exponential synchronization of reaction-diffusion BAM recurrent fuzzy neural networks (FNNs) with infinite distributed delays on time scales is investigated. Applied Lyapunov functional and inequality skills, some sufficient criteria are established to guarantee the global robust exponential synchronization of reaction-diffusion BAM recurrent FNNs with infinite distributed delays on time scales. One example is given to illustrate the effectiveness of our results.

Highlights

The study on the artificial neural networks has attracted much attention because of their potential applications such as signal processing, image processing, pattern classification, quadratic optimization, associative memory, moving object speed detection, etc
Many kinds of models of neural networks have been proposed by some famous scholars. One of these important neural network models is the bidirectional associative memory (BAM) neural network models, which were first introduced by Kosko [ – ]
The dynamical behaviors such as uniqueness, global asymptotic stability, exponential stability and invariant sets and attractors of the equilibrium point or periodic solutions were investigated for BAM neural networks with different types of time delays

Summary

Introduction

The study on the artificial neural networks has attracted much attention because of their potential applications such as signal processing, image processing, pattern classification, quadratic optimization, associative memory, moving object speed detection, etc. Through iterations of forward and backward information flows between the two layers, it performs a twoway associative search for stored bipolar vector pairs and generalize the single-layer autoassociative Hebbian correlation to a two-layer pattern-matched heteroassociative circuits This class of networks possesses good application prospects in some fields such as pattern recognition, signal and image process, artificial intelligence [ ]. As one of the famous neural network models, it has attracted many attention in the past two decades [ – ] since the BAM model was proposed by Kosko The dynamical behaviors such as uniqueness, global asymptotic stability, exponential stability and invariant. To the best of our knowledge, few authors have considered the synchronization of reaction-diffusion recurrent fuzzy neural networks with delays and Dirichlet boundary conditions on time scales which is a challenging and important problem in theory and application. In this paper, we will investigate the global robust exponential synchronization of delayed reaction-diffusion BAM recurrent fuzzy neural networks (FNNs) on time scales as follows:

Tij μj

Ii pij rij

Proof Calculating the delta derivation of