Characteristics of period-adding bursting bifurcation without chaos in the Chay neuron model

A period-adding bursting sequence without bursting-chaos in the Chay neuron model is studied by bifurcation analysis. The genesis of each periodic bursting is separately evoked by the corresponding periodic spiking patterns through two period-doubling bifurcations, except for the period-1 bursting occurring via Hopf bifurcation. Hence, it is concluded that this period-adding bursting bifurcation without chaos has a compound bifurcation structure closely related to period-doubling bifurcations of periodic spiking in essence.