Dynamical stability analysis of multiple equilibrium points in time-varying delayed recurrent neural networks with discontinuous activation functions

This paper is concerned with the dynamical stability analysis of multiple equilibrium points in recurrent neural networks with time-varying delays and discontinuous activation functions. Based on the decomposition of state space, some sufficient conditions for the existence of multiple equilibrium points are established, which ensure that n-dimensional recurrent neural networks with k-level discontinuous activation functions can have kn equilibrium points. Under these conditions, the equilibrium points are locally exponentially stable. Moreover, some conditions for the existence of sets of stable equilibrium points and unstable equilibrium points are derived for recurrent neural networks without delay and with discontinuous activation functions. Finally, three examples are given to illustrate the effectiveness of the results.