Dynamical Analysis and Multistability in a Neuronal System with Discrete and Distributed Delays

Abstract

In this article, a two-neuron system is founded having discrete and distributed delays. The system illustrates the multistability with two-coexisting of equilibrium and three-coexisting of two equilibria and one periodic activity. Through the pitchfork bifurcation, the stable equilibrium (0, 0, 0, 0) can evolve into two stable nontrivial equilibria, which is a two-coexisting of equilibrium. Further, the stable trivial equilibrium loses the stability with delay increasing. Employing the Hopf bifurcation, the delayed two-neuron system model obtains a periodic activity. Lastly, the neural system illustrates a three-coexisting with two equilibria and one periodic activity when the system's parameters pass through the pitchfork and Hopf bifurcations, which is a multistability induced by the discrete and distributed delays.