Time-delay effect on the bursting of the synchronized state of coupled Hindmarsh-Rose neurons.

The time-delay effect on the bursting of the synchronized state of coupled Hindmarsh-Rose neurons is investigated in this paper. The time-delay influence on the structure of the slow manifold is first studied by using the method of stability switch. And then on the basis of the geometric singular perturbation theory, case studies are given to show that the time delay can suppress the bursting oscillation or lead to more complex dynamics. In particular, the mechanism of the transition from bursting oscillation to relaxation oscillation and to chaotic bursting is stated. Numerical results are given to demonstrate the validity of the analytical results.