Delay-dependent multistability in recurrent neural networks.

Abstract

In this article, we focus on the delay-dependent multistability in recurrent neural networks. By constructing Lyapunov functional and using matrix inequality techniques, a novel delay-dependent multistability criterion is derived. The obtained results are more flexible and less conservative than previously known criteria. Two examples are given to show the effectiveness of the obtained criteria. Furthermore, some interesting delay-dependent dynamic behaviors have been showed in a special case, for example, we find that there is the coexistence of stable equilibria and stable limit cycles in the single neuron. Also, when the neurons are coupled, then the stable patterns are more complex.