Hopf Bifurcation Analysis of a Time Fractional Delayed Inertial BAM Neural Networks With Anisotropic Diffusion

ABSTRACT To better simulate the neurons of the human brain and deeply analyze the effects of various factors that may induce oscillations on neurodynamic behaviors, this study investigates a class of bidirectional associative memory neural networks (BAMNNs) with multiple time delays, the Caputo time fractional order, inertial terms, and anisotropic diffusion. Subsequently, the restrictions associated with bifurcation properties in the Caputo fractional‐order delayed inertial BAM neural networks with anisotropic diffusion (CFDIADBAMNNs) were resolved. Through analysis and derivation, the local stability criteria for the trivial uniformly steady state of the system are established. The flow graph method is employed to handle the high‐dimensional characteristic determinant in the theoretical analysis, and the analytical expression of the bifurcation point is explicitly derived. Finally, numerical simulations are conducted to verify the theoretical results. By selecting the time delay as the bifurcation parameter, the Hopf bifurcation characteristics of the system are determined. Meanwhile, it establishes that the anisotropic ratio of diffusion coefficients is the key governing factor determining the steady‐state spatial configuration of the system.