Delay-induced periodic oscillation for fractional-order neural networks with mixed delays

Abstract

This article is mainly devoted to the investigation on the stability and Hopf bifurcation of fractional-order neural networks with mixed delays. Applying a suitable substitution of variable, a novel equivalent fractional-order neural networks concerning single delay is set up. By analyzing the corresponding characteristic equation of the involved fractional-order delayed neural networks and choosing the time delay as bifurcation parameter, we derive a new sufficient condition to guarantee the stability behavior and the appearance of Hopf bifurcation for the considered fractional-order delayed neural networks. The study reveals that the time delay is a key factor which has a vital impact on stability and Hopf bifurcation of neural networks. The obtained results of this work can be effectively applied to design neural networks. The numerical simulations and bifurcation diagrams are displayed to verify the rationality of the analytical results.