Dynamical Behaviors in Coupled FitzHugh-Nagumo Neural Systems with Time Delays

It is observed that neuron encodes and integrates information employing a variety of complex dynamical behavior, such as spiking, bursting, periodicity, quasi-periodicity, and chaos. Time delay is an inevitable factor in the signal transmission between neurons, and neural system may lose its stability even for very small delay. In this paper, a model of coupled FitzHugh-Nagumo (FHN) neural system with two different delays is formulated, and its nonlinear dynamic behaviors such as stability, bifurcations, and chaos are then studied. It is shown that time delays can affect the stability of equilibrium states, and thereby lead to Hopf bifurcation and oscillation behavior. Moreover, some complex dynamics including quasi-periodic solutions and chaos are numerically demonstrated. Subsequently, numerical examples illustrate the effectiveness and feasibility of the theoretical results.