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

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.

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