On fractional ring neural networks with multiple time delays: Stability and Hopf bifurcation analysis

Abstract

Stability and Hopf bifurcation analysis of neural networks have become popular topics in recent years. In this paper, a large-scale fractional ring neural network with multiple time delays is considered. The model comprises three rings that share a single node. The effects of time delay and fractional order on its stability and Hopf bifurcation have been investigated. Firstly, the characteristic equation is obtained by using the Laplace transform. Then, the time delay and fractional order are set as a bifurcation parameter respectively. Correspondingly, the local stability and Hopf bifurcation conditions are derived by analyzing the characteristic equations. Finally, two examples are given to support the theoretical analysis. In fact, this article provides an effective method for analyzing the stability and Hopf bifurcation of fractional ring neural networks.