Stability and Hopf-Bifurcation Analysis of Delayed BAM Neural Network under Dynamic Thresholds

Abstract

In this paper the dynamics of a three neuron model with self-connection and distributed delay under dynamical threshold is investigated. With the help of topological degree theory and Homotopy invariance principle existence and uniqueness of equilibrium point are established. The conditions for which the Hopf-bifurcation occurs at the equilibrium are obtained for the weak kernel of the distributed delay. The direction and stability of the bifurcating periodic solutions are determined by the normal form theory and central manifold theorem. Lastly global bifurcation aspect of such periodic solutions is studied. Some numerical simulations for justifying the theoretical analysis are also presented.