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Bursting Oscillations near Codimension-Two Bifurcations in the Chay Neuron Model

It is important to study neural firing patterns based on bifurcation scenarios of neurons. In this paper, the transition mechanisms of different firing types in the Chay neuron model arc investigated by using two-parameter bifurcations and fast/slow dynamic analysis, in which special attention is paid to the codim-2 bifurcations related to the change of bursting types. It is concluded that the codim-2 cusp (CP) bifurcation is essential to the "fold/fold" bursting oscillation. Moreover, there are also two types of bursting oscillations near the codim-2 Bogdanov-Takens (BT) bifurcation, that is, "fold/Hopf' bursting and "fold/homoclinic" bursting.