Comparative analysis on Hopf bifurcation of integer‐order and fractional‐order two‐neuron neural networks with delay

Abstract

Summary This article mainly focuses on the stability and the existence of Hopf bifurcation of integer‐order and fractional‐order two‐neuron neural networks with delay. First of all, we obtain the sufficient criterion to ensure the stability and the existence of Hopf bifurcation of integer‐order two‐neuron neural networks with delay. Next, we establish the sufficient condition guaranteeing the stability and the existence of Hopf bifurcation of fractional‐order two‐neuron neural networks with delay. The study reveals that the time delay has a vital effect on the stability and Hopf bifurcation of integer‐order and fractional‐order two‐neuron neural networks with delay. By comparative analysis on Hopf bifurcation for integer‐order and fractional‐order two‐neuron neural networks with delay, we find that under an appropriate parameter conditions, the stability region can be enlarged, and the time of appearance of Hopf bifurcation of the involved two‐neuron neural networks can be postponed by using fractional‐order case. Finally, computer simulation results are presented to illustrate the theoretical findings. The established results of this article play an important role in designing and controlling networks.

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