Multistability of memristive Cohen–Grossberg neural networks with non-monotonic piecewise linear activation functions and time-varying delays

Abstract

The problem of coexistence and dynamical behaviors of multiple equilibrium points is addressed for a class of memristive Cohen–Grossberg neural networks with non-monotonic piecewise linear activation functions and time-varying delays. By virtue of the fixed point theorem, nonsmooth analysis theory and other analytical tools, some sufficient conditions are established to guarantee that such n-dimensional memristive Cohen–Grossberg neural networks can have 5n equilibrium points, among which 3n equilibrium points are locally exponentially stable. It is shown that greater storage capacity can be achieved by neural networks with the non-monotonic activation functions introduced herein than the ones with Mexican-hat-type activation function. In addition, unlike most existing multistability results of neural networks with monotonic activation functions, those obtained 3n locally stable equilibrium points are located both in saturated regions and unsaturated regions. The theoretical findings are verified by an illustrative example with computer simulations.