Dynamical Bifurcation of Large-Scale-Delayed Fractional-Order Neural Networks With Hub Structure and Multiple Rings

The dynamics of neural networks has been widely concerned by scholars. However, most of the previous results on dynamical bifurcations are limited to few nodes coupling neural networks which modeled by differential equations with integer-order derivative, and few efforts have been contributed to studying the bifurcation behaviors of large-scale fractional-order neural networks. Furthermore, the structural characteristics of networks are also of great research value. Among them, the ring structure is a common phenomenon in neural networks. Although there are few papers on the bifurcation analysis of ring-structured neural networks recently, they consider only the case of a single ring. In this article, the dynamical analysis and design for a class of large-scale-delayed fractional-order neural networks with multiple rings and hub structure are investigated. First, the time delay is considered to be the bifurcation parameter and the formula of Coates’ flow graph is adopted to obtain the characteristic equation of large-scale networks. Second, by analyzing the complex radial and circular connections of neurons, the delay-induced Hopf bifurcation sufficient conditions for the neural network are established. Finally, the theoretical results are substantiated by a number of numerical simulation experiments and the relationships between the onset of bifurcation and the fractional order, the number of neurons, and the number of rings are revealed.