Stability switches and fold-Hopf bifurcations in an inertial four-neuron network model with coupling delay

The dynamics of a four-neuron delayed bidirectional associative memory (BAM) model with inertia are investigated. Local stability for the trivial equilibrium is analyzed for various system parameters. Stability switches and fold-Hopf bifurcations are found to occur in this model as progressive increasing of coupling delay values. Fold-Hopf bifurcations are completely analyzed in the parameter space of the coupling delay and the connection weight by employing the extended perturbation-incremental scheme. Various dynamical behaviors are qualitatively classified in the neighbor of fold-Hopf bifurcation point and bifurcating periodic solutions are expressed analytically in an approximate form. The validity of the results is shown by their consistency with the numerical simulation.