Stability Analysis of Fractional-Order Bidirectional Associative Memory Neural Networks with Mixed Time-Varying Delays

Zhanying Yang,Jie Zhang

doi:10.1155/2019/2363707

Abstract

This paper studies the stability analysis of fractional-order bidirectional associative memory neural networks with mixed time-varying delays. The orders of these systems lie in the interval 1,2. Firstly, a sufficient condition is derived to ensure the finite-time stability of systems by resorting to some analytical techniques and some elementary inequalities. Next, a sufficient condition is obtained to guarantee the global asymptotic stability of systems based on the Laplace transform, the mean value theorem, the generalized Gronwall inequality, and some properties of Mittag–Leffler functions. In particular, these obtained conditions are expressed as some algebraic inequalities which can be easily calculated in practical applications. Finally, some numerical examples are given to verify the feasibility and effectiveness of the obtained main results.

Highlights

Neural networks have drawn increasing interests due to their powerful applications in physics, mechanics, biology, information science, and sociology In order to meet the requirements in practical applications, some researchers have proposed various types of neural networks, such as cellular neural networks [1], Hop eld neural networks [2], recurrent neural networks [3], bidirectional associative memory (BAM) neural networks [4], and memristor-based neural networks [5]
We focus on a class of Caputo fractionalorder BAM neural networks with discrete and distributed time-varying delays for α ∈ (1, 2). ese networks can be described as
We focus on a class of fractionalorder BAM neural networks with discrete and finite-time distributed time-varying delays for α ∈ (1, 2)

Summary

Introduction

Neural networks have drawn increasing interests due to their powerful applications in physics, mechanics, biology, information science, and sociology In order to meet the requirements in practical applications, some researchers have proposed various types of neural networks, such as cellular neural networks [1], Hop eld neural networks [2], recurrent neural networks [3], bidirectional associative memory (BAM) neural networks [4], and memristor-based neural networks [5]. Xu et al [20] considered the finite-time stability for a class of fractional-order BAM delayed neural networks. Lots of researchers have made great efforts to the dynamics of neural networks with both discrete and distributed delays and there have been some excellent results [33,34,35,36,37,38] Notice that these works were mainly concerned with integer-order neural networks. Zhang et al [41] investigated the asymptotic stability for a class of Riemann–Liouville fractional-order neural networks with discrete and finite-time distributed constant delays. E main contributions of this paper include the following several aspects: (i) We consider the stability analysis for a class of fractional-order BAM neural networks with discrete and distributed timevarying delays for α ∈ (1, 2) which has not been discussed in the existing literature.

Preliminaries and Network Model

Main Results

Numerical Simulations