Input-to-State Stability of Stochastic Memristive Neural Networks with Time-Varying Delay

Xu Y Lou,Qian Ye

doi:10.1155/2015/140857

Abstract

This paper is concerned with the input-to-state stability problem of a class of memristive neural networks. We consider the neural networks that take into account both the stochastic effects and time-varying delay, and introduce the notions of meansquare exponential input-to-state stability. Using the stochastic analysis theory and Itô formula for stochastic differential equations, we establish sufficient conditions for both mean-square exponential input-to-state stability and mean-square exponential stability. Numerical simulations are also provided to demonstrate the theoretical results.

Highlights

In the recent years, the memristor-based or memristive neural network models have been extensively investigated and successfully applied to function approximation [1], associative memory [2], chaos synchronization [3], and image processing [4]
Due to the existence of time delays, the stability issue in delayed memristive neural networks becomes one of the most important problems and there have been many stability results on delayed memristive neural networks reported in the literature; for instance, see [5,6,7,8,9] and references therein
We present sufficient conditions for mean-square exponential input-to-state stability (eISS) and the mean-square exponential stability based on the stochastic analysis theory and Itoformula

Summary

Introduction

The memristor-based or memristive neural network models have been extensively investigated and successfully applied to function approximation [1], associative memory [2], chaos synchronization [3], and image processing [4]. Exponential stability was addressed in [6] for a class of stochastic memristor-based recurrent neural networks with time-varying delays. The authors in [7] considered the exponential dissipativity of memristor-based recurrent neural networks with time-varying delays. The recent work of [11] presented sufficient conditions for mean-square exponential ISS of stochastic delayed neural networks, but the synaptic weights are constants. We attempt to construct SMNNs with timevarying delay and focus on the mean-square exponential input-to-state stability (eISS). The proposed method is applicable to deal with the synchronization problem of SMNNs. We present sufficient conditions for mean-square eISS and the mean-square exponential stability based on the stochastic analysis theory and Itoformula. ∞, where E[⋅] stands for the correspondent expectation operator with respect to the given probability measure P

Model Description and Preliminaries

Main Results

Example

Conclusions