Hopf–Pitchfork bifurcation in a simplified BAM neural network model with multiple delays

Abstract

In this paper, a simplified BAM neural network model with multiple delays is considered. By studying the distribution of the eigenvalues of the associated characteristic equation, we derive the critical values where Hopf–Pitchfork bifurcation occurs. Then, by computing the normal forms for the system, the bifurcation diagrams are obtained. Furthermore, we carry out bifurcation analysis and numerical simulations showing that there exist a stable fixed point, a pair of stable fixed points, a stable periodic solution, and co-existence of a pair of stable periodic solution in the neighborhood of the Hopf–Pitchfork critical point.