Comparative analysis on bifurcation of four-neuron fractional ring networks without or with leakage delays

Abstract

This paper is concerned with the problem of bifurcation for a ring fractional Hopfield neural network with leakage time delay and communication time delay. The stability and the Hopf bifurcations of such a network without and with time delays are investigated by analyzing the associated characteristic equations. Specifically, some criteria for the occurrence of Hopf bifurcations at the trivial steady state are established. It is shown that the dynamical property of the network is not only crucially dependent on the communication time delay, but also significantly influenced by the leakage time delay. Furthermore, the effects of the order on the Hopf bifurcation are numerically demonstrated. Finally, four numerical examples are provided to illustrate the feasibility of the theoretical results.