Further investigation on bifurcation and their control of fractional‐order bidirectional associative memory neural networks involving four neurons and multiple delays

Abstract

This work principally probes into the stability, the existence, and control of Hopf bifurcation of new established fractional‐order delayed bidirectional associative memory (BAM) neural networks with four neurons. Firstly, based on the earlier study, we set up a class of new fractional‐order multiple delayed BAM neural networks with four neurons. Secondly, applying an appropriate variable transformation, we get a new equivalent fractional‐order single delayed BAM neural networks with four neurons. With the aid of the stability theory and bifurcation knowledge of fractional‐order differential dynamical systems, a novel sufficient criterion to guarantee the stability and the appearance of Hopf bifurcation of the addressed fractional‐order delayed BAM neural networks is set up. Thirdly, designing a suitable time‐delayed feedback controller, the stability region and the time of appearance of Hopf bifurcation for the involved neural networks have been adjusted. Finally, two simulation examples are presented to illustrate the rationality of the mathematical derivation results. The study vindicates that the time delay has great effect on the stability, bifurcation, and its control for involved network models. The obtained fruits of this work can be effectively applied to control and design neural networks. Also, some research ideas will play a key role in studying the related fractional‐order dynamical models in actual world.