Multistability of delayed neural networks with monotonically nondecreasing linear activation function

Abstract

This paper investigates the multistability on a class of delayed neural networks with monotonically nondecreasing linear activation function. For n state neurons with 2m+1 piecewise linear activation function, we prove the neural networks have (2m+1)n equilibrium points, (m+1)n of which are locally exponentially stable. Different from the traditional multistability analysis method such as fixed point theory, this paper only uses the character of activation functions, and can also handle the neural networks with disturbance term. The research results of this paper generalize the previous related research works and are easy to test. A numerical example is given to shown the effectiveness of our theoretical results.