Passivity of Memristive BAM Neural Networks with Probabilistic and Mixed Time-Varying Delays

Weiping Wang,Xiong Luo,Meiqi Wang,Lixiang Li,Wenbing Zhao

doi:10.1155/2018/5830160

Abstract

This paper is concerned with the passivity problem of memristive bidirectional associative memory neural networks (MBAMNNs) with probabilistic and mixed time-varying delays. By applying random variables with Bernoulli distribution, the information of probability time-varying delays is taken into account. Furthermore, we consider the probability distribution of the variation and the extent of the delays; therefore, the results derived are less conservative than in the existing papers. In particular, the leakage delays as well as distributed delays are all taken into consideration. Based on appropriate Lyapunov-Krasovskii functionals (LKFs) and some useful inequalities, several conditions for passive performance are established in linear matrix inequalities (LMIs). Finally, numerical examples are given to demonstrate the feasibility of the presented theories, and the results reveal that the probabilistic and mixed time-varying delays have an unstable influence on the system and should not be ignored.

Highlights

Bidirectional associative memory neural networks (BAMNNs) are a class of two-layer neural systems, which were first introduced by Kosko in 1987
Zhang et al considered the exponential stability of BAMNNs with time-varying delays in [8]
We propose the memristive bidirectional associative memory neural networks (MBAMNNs) with probabilistic time-varying delays as follows: m xi (t) = −Cixi (t) + ∑aji (xi (t)) fj (yj (t))

Summary

Introduction

Bidirectional associative memory neural networks (BAMNNs) are a class of two-layer neural systems, which were first introduced by Kosko in 1987. In 2016, Pradeep et al investigated the robust stability analysis of stochastic neural networks with probabilistic time-varying delays in [36]. Li et al considered passivity analysis of memristive neural networks with probabilistic time-varying delays in [37]. Under the influence of leakage and additive time-varying delays, robust passivity analysis for neural networks was addressed in [40]. To the best of our knowledge, there are few results on the passivity of MBAMNNs with probabilistic, leakage, and distributed time-varying delays. (1) This is the first attempt to discuss the passivity analysis of MBAMNNs with probabilistic and mixed time-varying delays.

Model Description and Preliminaries

Main Results

Numerical Simulation

Conclusion