Dynamical bifurcations in a delayed fractional‐order neural network involving neutral terms

Abstract

The stability and bifurcations of a fractional‐order neural network with a neutral delay are nicely contemplated with the help of the Cramer's rule. The three‐neuron neutral‐type fractional‐order neural network (NTFONN) is firstly constructed. Secondly, the Laplace transform of the Caputo fractional‐order derivatives is used. Afterward, using the analytical method of characteristic equations and Cramer's rule, the existence of Hopf bifurcations is obtained. Moreover, it indicates that the neutral delay plays an enormously significant role in remaining network stabilization and controlling the occurrence of Hopf bifurcations in NTFONN. It further detects that the devised NTFONN has outstanding stability performance in comparison with the corresponding integer‐order one. Finally, numerical simulations are developed to confirm the feasibility and validity of the obtained results.