Design of bursting in two-dimensional discrete-time neuron models

We propose a design method for bursting neuron models with a specified average angular frequency and duty ratio by using the bifurcation theory . There are some pairs of two-periodic points in the models. When a Hopf bifurcation for the two-periodic points occurs, there exist two pairs of non-isolated invariant closed curves surrounding each two-periodic point. The proposed design method derives parameters and initial conditions in the models. We also show the effectivity of the proposed design method by simulation.