Stability of bifurcating periodic solutions for a single delayed inertial neuron model under periodic excitation

Using the averaged method, we investigate the dynamical characteristics of a single inertial neuron model with time delay under periodic external stimuli. It is shown that the system will lose its stability when the time delay is increased and will give rise to a quasi-periodic motion and chaos under the interaction of the periodic excitation. Numerical simulations show that the results of the analytical method are correct by a comparison with those of direct numerical integration.