Abstract
Tonically spiking as well as bursting neurons are frequently observed in electrophysiological experiments. The theory of slow–fast dynamical systems can describe basic scenarios of how these regimes of activity can be generated and transitions between them can be made. Here, we suggest a biophysically plausible mechanism based on homoclinic bifurcations of a saddle periodic orbit which explains a transition between tonic spiking behavior and bursting behavior in a neuron model of Hodgkin–Huxley type. Also, this mechanism is featured by the coexistence of tonic spiking and bursting oscillations.
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