Dynamical Bifurcations in a Fractional-Order Neural Network with Nonidentical Communication Delays

Although the number of investigation fruits on neural networks is growing explosively, the majority of such research effort is devoted to integer-order neural networks, while only a few are on fractional-order neural networks (FONNs). By arguing the associated characteristic equation of the proposed network, we establish delay-dependent stability conditions and the bifurcation point. Then selecting the communication delay as the bifurcation parameter and the other delay as the constant in its stability interval, the conditions for the occurrence of Hopf bifurcation are established. Then, we confirm the conditions by numerical simulation. It is indicated that the stability of the FONN remains unchanged with the lesser control delay, and will not exist once the delay outnumbers its critical value. And we discover that compared with integer-order neural networks the convergence time to the equilibrium point of FONN is shorter for the same system parameters. It detects that fractional orders are able to advance(postpone) the generation of the bifurcations of the developed FONN. The paper demonstrates that the fractional orders have significant effects on the stability of the FONN. Finally, the theoretical results are authenticated by numerical simulations.