On multistability of competitive neural networks with discontinuous activation functions

Abstract

In this paper, we examine the problem of multi-stability for competitive neural networks associated with discontinuous non-monotonic piecewise linear activation functions. First, we derive certain sufficient conditions for coexistent multiple equilibrium points, which reveals that the n-neuron competitive neural networks under study can possess as many as 4n equilibrium points. Next, we investigate local stability of those multiple equilibrium points, which shows that 3n equilibrium points are locally stable. The new multistability results are obtained by virtue of the fixed point theorem and the theory of strict diagonal dominance matrix. The theoretical results are finally validated by a numerical example along with computer simulations.