Design of bursting in a two-dimensional discrete-time neuron model

Alternating a quiescent state and a spiking one in a neuron is called bursting, which is one of important neuron activities. In this Letter, we will propose a simple design method for a bursting neuron model with a specified period and duty ratio of the bursting based on bifurcation theory. The neuron model has been proposed by the author et al. based on Aihara's chaotic neuron model. Mechanism of generating the bursting in the neuron model is a quasi-periodic oscillation with respect to internal states, which is caused from a Hopf bifurcation for a pair of two-periodic points. We also show an example derived by the proposed design method.