Insight into Hopf Bifurcation and Control Methods in Fractional Order BAM Neural Networks Incorporating Symmetric Structure and Delay

The trait of solution, bifurcation mechanism, and stability of delayed BAM neural network models have attracted great attention from many scholars. But the exploration about the stability aspect and bifurcation mechanism of fractional delayed BAM neural network models is relatively few. This work will focus on the stability aspect and bifurcation mechanism of fractional delayed BAM neural network models. Lipschitz condition, Laplace transform, construction of a proper function, stability criterion, and bifurcation principle of fractional delayed dynamical system, delayed feedback controller, dislocated feedback controller, and Matlab simulation technique are exploited. The criteria on the boundedness, existence, and uniqueness of solutions to fractional delayed BAM neural network models are gained. A new delay-independent bifurcation criterion and stability of the formulated neural network models is acquired. Delayed feedback controller and dislocated feedback controller are effectually utilized to dominate the time of generation of bifurcation and stability domain of the formulated neural network models. MATLAB simulation experiments are provided to substantiate the acquired primary outcomes. The gained theoretical outcomes of this article possess tremendous theoretical significance in devising and running the fractional delayed BAM neural network models.