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 5
ⁿ
equilibrium points. Then, with the aid of the theories of set-valued maps and differential inclusions, the exponential stability is proved for 3
ⁿ
equilibrium points out of those 5
ⁿ
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.