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

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 5 n equilibrium points, among which 3 n 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 3 n 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.