Bifurcations in a fractional-order BAM neural network with four different delays

This paper illuminates the issue of bifurcations for a fractional-order bidirectional associative memory neural network(FOBAMNN) with four different delays. On account of the affirmatory presumption, the developed FOBAMNN is firstly transformed into the one with two nonidentical delays. Then the critical values of Hopf bifurcations with respect to disparate delays are calculated quantitatively by establishing one delay and selecting remaining delay as a bifurcation parameter in the transformed model. It detects that the stability of the developed FOBAMNN with multiple delays can be fairly preserved if selecting lesser control delays, and Hopf bifurcation emerges once the control delays outnumber their critical values. The derived bifurcation results are numerically testified via the bifurcation graphs. The feasibility of theoretical analysis is ultimately corroborated in the light of simulation experiments. The analytic results available in this paper are beneficial to give impetus to resolve the issues of bifurcations of high-order FONNs with multiple delays. (C) 2021 Elsevier Ltd. All rights reserved.

Automated summary

This paper investigates the bifurcation issue of a FOBAMNN with four different delays, finding that the stability of the network can be preserved by selecting smaller control delays, while Hopf bifurcation occurs once the delays exceed their critical values. The derived bifurcation results are numerically verified and the theoretical analysis is validated through simulation experiments.