Bifurcation analysis in a discrete BAM network model with delays

In this paper, a discrete bidirectional associative memory network model consisting of three neurons is considered. We study the stability of the equilibria of the system by analysing the distribution of the eigenvalues. It is found that there are three kinds of bifurcations: Pitchfork bifurcation, Period-Doubling bifurcation and Neimark–Sacker bifurcation. The direction and stability of the Neimark–Sacker are determined by using normal forms and centre manifold theory. Some numerical simulations are carried out to illustrate the analytical results.

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