Multistability of memristive neural networks with non-monotonic piecewise linear activation functions

Abstract

In this paper, a general class of non-monotonic piecewise linear activation functions is introduced and then the coexistence and dynamical behaviors of multiple equilibrium points are studied for a class of memristive neural networks (MNNs). It is proven that under some conditions, such n-neuron MNNs can have 5n equilibrium points located in Rn, and 3n of them are locally exponentially stable, by means of fixed point theorem, nonsmooth analysis theory and rigorous mathematical analysis. The investigation shows that the neural networks with nonmonotonic piecewise linear activation functions introduced in this paper can have greater storage capacity than the ones with Mexican-hat-type activation function.