Further exploration on bifurcation of fractional-order six-neuron bi-directional associative memory neural networks with multi-delays

Abstract

This study mainly explores fractional-order six-neuron bi-directional associative memory (BAM) neural networks involving multi-delays. Taking advantage of contraction mapping principle, we prove that the solution of the addressed BAM neural networks exists and is unique. Utilizing a acceptable function, we confirm that the solution of the addressed BAM neural networks is bounded. By applying a suitable variable substitution, new fractional order six-neuron BAM neural networks involving mult-delays are converted to a class of fractional order six-neuron BAM neural networks with single delay. Using the stability criterion and bifurcation theory of fractional order differential dynamical systems, we carry out a detailed discussion on the stability and the onset of Hopf bifurcation of the established BAM neural networks. The study shows that the time delay is an important factor which affects the stability behavior and Hopf bifurcation of the involved neural networks. Numerical simulation plots are presented to illustrate our derived key conclusions. The derived analytical findings of the study play a vital role in optimizing and designing neural networks.