Stability and Bifurcation control of Fractional BAM Neural Networks with Diffusion and Time Delays

Based on fractional calculus theory and reaction-diffusion equation theory, a fractional-order time-delay reaction-diffusion neural network with Neumann boundary conditions is investigated. By constructing the phase space basis based on the Laplace operator eigenvector, the system equation is linearized to obtain the characteristic equation. Then, the characteristic equation is analyzed, and the local stability of the system at the equilibrium point is discussed. And taking the time delay as the bifurcation parameter, the stability changes of the system at the equilibrium point and the generation conditions of the Hopf bifurcation are studied when the time delay changes. Moreover, a state feedback controller is designed to control the bifurcation of the system. Finally, the theoretical derivation is verified by numerical simulation.