On stability of multiple equilibria for delayed neural networks with discontinuous activation functions

Abstract

This paper considers the stability problem of multiple equilibria for delayed neural networks with discontinuous activation functions. By virtue of the fixed point theorem, it is found that under some sufficient conditions, n neurons delayed neural networks with discontinuous non-monotonic activation functions can have at least 4™ equilibrium points and 3™ of them are locally stable. Furthermore, it is shown that the storage capacity of the neural networks can be considerably expanded by use of discontinuous activation functions, which is important in several neural network applications. Finally, the effectiveness of the theoretical findings is verified by a numerical example.