Exploration of bifurcation for a fractional-order BAM neural network with n+2 neurons and mixed time delays

Abstract

This article aims to deal with the stability and Hopf bifurcation analysis for a type of fractional-order bidirectional associative memory (BAM) neural network involving two neurons in the X-layer and n neurons in the Y-layer, respectively. In view of the universal existence and multiplicity of time delay in many real systems, leakage delay and nonuniform communication delays are both taken into account. Coates’s flow-graph formula is efficiently adopted to solve the high-order characteristic equation of the associated linearized system. By making some assumptions on the mixed time delays, the obtained characteristic equation only contains the leakage delay, which is selected as the bifurcation parameter. Utilizing the discriminated criteria of stability for fractional-order dynamical systems and Hopf bifurcation theory, we obtain the critical value of the bifurcation point, greater than which the Hopf bifurcation would occur. Particularly, the stability and Hopf bifurcation is also analyzed for the case of no leakage delay to get an insight into the effect of the leakage delay. Finally, the validity of our theoretical results is substantiated through a simulation example.