Exponential stability of multiple equilibria for memristive Cohen-Grossberg neural networks with non-monotonic activation functions

This paper is concerned with the problem of exponential stability of multiple equilibria for memristive Cohen-Grossberg neural networks with non-monotonic piece-wise linear activation functions. First, the fixed point theorem and nonsmooth analysis theory are applied to develop some sufficient conditions under which n-dimensional memristive Cohen-Grossberg neural networks with non-monotonic activation functions are ensured to have 5ⁿ equilibrium points. Then, with the aid of the theories of set-valued maps and differential inclusions, the exponential stability is proved for 3ⁿ equilibrium points out of those 5ⁿ equilibrium points. The importance of the multistability results obtained in this paper lies in that the use of the proposed non-monotonic activation functions can increase the storage capacity of the corresponding neural networks considerably.