Comparative exploration on bifurcation behavior for integer-order and fractional-order delayed BAM neural networks

In the present study, we deal with the stability and the onset of Hopf bifurcation of two type delayed BAM neural networks (integer-order case and fractional-order case). By virtue of the characteristic equation of the integer-order delayed BAM neural networks and regarding time delay as critical parameter, a novel delay-independent condition ensuring the stability and the onset of Hopf bifurcation for the involved integer-order delayed BAM neural networks is built. Taking advantage of Laplace transform, stability theory and Hopf bifurcation knowledge of fractional -order differential equations, a novel delay-independent criterion to maintain the stability and the appearance of Hopf bifurcation for the addressed fractional-order BAM neural networks is established. The investigation indicates the important role of time delay in controlling the stability and Hopf bifurcation of the both type delayed BAM neural networks. By adjusting the value of time delay, we can effectively amplify the stability region and postpone the time of onset of Hopf bifurcation for the fractional-order BAM neural networks. Matlab simulation results are clearly presented to sustain the correctness of analytical results. The derived fruits of this study provide an important theoretical basis in regulating networks.

Automated summary

The present study investigates the stability and onset of Hopf bifurcation in two types of delayed BAM neural networks (integer-order and fractional-order). A novel delay-independent condition for ensuring stability and Hopf bifurcation onset in integer-order delayed BAM neural networks is proposed, and a delay-independent criterion based on Laplace transform, stability theory, and Hopf bifurcation of fractional-order differential equations is established for maintaining stability and the appearance of Hopf bifurcation in fractional-order BAM neural networks. The study highlights the significant role of time delay in controlling network stability and Hopf bifurcation. By adjusting the value of time delay, the stability region can be effectively enlarged and the time of Hopf bifurcation onset can be delayed for fractional-order BAM neural networks. Matlab simulation results are provided to validate the analytical findings. The results of this study provide an important theoretical basis for network regulation.