Further analysis on dynamical properties of fractional‐order bi‐directional associative memory neural networks involving double delays
Changjin Xu, Wei Zhang, Chaouki Aouiti, Zixin Liu, Lingyun Yao
Abstract
In this study, a class of novel fractional‐order bi‐directional associative memory (BAM) neural networks involving double time delays are put up and investigated. First of all, we prove that the solution of the involved neural networks exists and is unique and bounded. Second of all, we investigate the stability behavior and the onset of Hopf bifurcation of the involved network models by applying the stability theory and the related Hopf bifurcation knowledge on fractional‐order differential equations. A sufficient condition to ensure the stability and onset of Hopf bifurcation of the considered network models is established. The importance of time delay in dynamical behavior of the fractional‐order delayed BAM neural networks has been displayed. Lastly, computer simulations with Matlab software are presented to test the effectiveness of the established theoretical results. The obtained analysis fruits of this manuscript play a vital role in designing and controlling networks.