Bursting and two-parameter bifurcation in the Chay neuronal model

Lixia Duan，Zhuoqin Yang，Shenquan Liu

In this paper, we study and classify the firing patterns in the Chay neuronal model by the fast/slow decomposition and the two-parameter bifurcations analysis. We show that the Chay neuronal model can display complex bursting oscillations, including the fold/fold bursting, the Hopf/Hopf bursting and the Hopf/homoclinic bursting. Furthermore, dynamical properties of different firing activities of a neuron are closely related to the bifurcation structures of the fast subsystem. Our results indicate that the codimension-2 bifurcation points and the related codimension-1 bifurcation curves of the fast-subsystem can provide crucial information to predict the existence and types of bursting with changes of parameters.

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