Bifurcation analysis and sliding mode control of fractional-order BAM neural network with multiple delays

This paper investigates the bifurcation dynamics behavior of a fractional-order five-dimensional bidirectional associative memory neural network model incorporating multiple delays. Selecting the delay as the bifurcation parameter, the critical delay thresholds for the onset of Hopf bifurcation are derived through characteristic equation analysis. Furthermore, the interplay between independent and coupled delay effects is systematically explored, and bifurcation mechanisms under various delay interaction modes are discussed. To address oscillatory behavior typically observed after the bifurcation, a sliding mode control scheme is designed to ensure the asymptotic stability of the system. Finally, simulation results demonstrate the validity of the theoretical results and confirm the effectiveness of the control scheme in suppressing oscillatory divergence.