Bifurcation analysis of a fractional-order Cohen-Grossberg neural network with three delays

This paper pays more attention to the dynamic bifurcations of a fractional -order Cohen- Grossberg neural network in the sense of the Caputo fractional derivative with three delays. In the beginning, the dynamical behaviors of the system in several different cases are discussed when time delay can be viewed as zero, and the corresponding Hopf bifurcation critical values are derived. Subsequently, the system's dynamics with three delays are investigated for three cases where none are zero. The reduction method of transcendental terms is applied to solve the third transcendental term in the characteristic equation. The exact bifurcation conditions are obtained by choosing one of the delays as the bifurcation parameter, respectively. It is worth noting that previous studies on multi -delay systems only discuss the case where the multi -delay can be transformed into a single delay or two delays based on certain transformations. This paper explores how to study the problem of a system with three delays without transforming the delays. In addition, the effects of time delays on the critical points of the system are examined. Finally, to verify the correctness of the proposed results, numerical simulations are addressed.