Hopf Bifurcation of Fractional-Order Complex-Valued BAM Neural Network under Feedback Control

In this paper, in order to achieve more accurate modelling of nonlinear and complex systems, we introduce complex-valued state and fractional-order integral operators into neural network and discuss the stability and Hopf bifurcation of complex-valued fractional-order bidirectional associative memory (BAM) neural network with two neurons. In addition, feedback controller is designed to achieve control of the Hopf bifurcation of the system to optimise and enhance the stability of the system. In this paper, the time-delay is used as the bifurcation parameter, the corresponding characteristic equations are analyzed, and the common region of the two curves is determined by using the method of combining numbers and shapes, and on the basis of which the sufficient criteria for judging the local stability of the system and the existence of the Hopf bifurcation are given in turn. At the end of the article, two numerical simulation examples are given, and the results show that the feedback controller can effectively control the Hopf bifurcation of the system, and enhance the stability performance of the system by increasing the critical value of the bifurcation of the time-delay.