Further Exploration on Bifurcation for Fractional-Order Bidirectional Associative Memory (BAM) Neural Networks concerning Time Delay∗

This work principally considers the stability issue and the emergence of Hopf bifurcation for a class of fractional-order BAM neural network models concerning time delays. Through the detailed analysis on the distribution of the roots of the characteristic equation of the involved fractional-order delayed BAM neural network systems, we set up a new delay-independent condition to guarantee the stability and the emergence of Hopf bifurcation for the investigated fractional-order delayed BAM neural network systems. The work indicates that delay is a significant element that has a vital impact on the stability and the emergence of Hopf bifurcation in fractional-order delayed BAM neural network systems. The simulation figures and bifurcation plots are clearly presented to verify the derived key research results. The established conclusions of this work have significant guiding value in regulating and optimizing neural networks.