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Bursting and two-parameter bifurcation in the Chay neuronal model. (English) Zbl 1229.34071

Summary: 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-two bifurcation points and the related codimension-one bifurcation curves of the fast-subsystem can provide crucial information to predict the existence and types of bursting with changes of parameters.

MSC:

34C60 Qualitative investigation and simulation of ordinary differential equation models
34C23 Bifurcation theory for ordinary differential equations
34E20 Singular perturbations, turning point theory, WKB methods for ordinary differential equations
92C20 Neural biology
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