Exploration of bifurcation and stability in a class of fractional-order super-double-ring neural network with two shared neurons and multiple delays

Abstract

Complex multi-ring coupling structures are common in real-world networks. However, the current work is mainly limited to unidirectional multi-ring or those sharing a neuron. This paper is devoted to the stability and Hopf bifurcation of a class of double-ring neural network with two shared neurons and multiple time delays, where n and m neurons are distributed on the double-ring, respectively. First, we obtain the characteristic equation of the network at the trivial equilibrium point by using the Coates flow graph method. Then, based on this, some sufficient conditions for the stability and Hopf bifurcation of the double-ring network under two connection modes are given. Finally, we provide some numerical examples to illustrate the validness of the theoretical results, and the influences of fractional order, network size and the distance between two shared neurons on Hopf bifurcation are also discussed.