Exponential stability of positive neural networks in bidirectional associative memory model with delays

Abstract

This paper is concerned with the problem of exponential stability of positive neural networks in bidirectional associative memory (BAM) model with multiple time-varying delays and nonlinear self-excitation rates. On the basis of a systematic approach involving extended comparison techniques via differential inequalities, we first prove the positivity of state trajectories initializing from a positive cone called the admissible set of initial conditions. In combination with the use of Brouwer's fixed point theorem and M-matrix theory, we then derive conditions for the existence and global exponential stability of a unique positive equilibrium of the model. An extension to the case of BAM neural networks with proportional delays is also presented. The effectiveness of the obtained results is illustrated by a numerical example with simulations. KEYWORDS exponential stability, M-matrix, positve BAM neural networks, time-varying delays MSC CLASSIFICATION 34 K20; 34 K45; 92C42

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