Stability and Hopf bifurcation in leech heart interneuron model

Document Type : Research Article


1 Department of Mathematics, Payame Noor University(PNU), Tehran, Iran.

2 Department of Mathematics, Faculty of Mathematical Sciences, University of Sharif, Tehran, Iran.


This article investigates the activity regimes of a realistic neuron model (as a slow-fast system). The authors study this model using the dynam-ical systems theory, for example, qualitative theory methods of slow-fast systems. The authors obtain the stability conditions of equilibria in leech heart interneurons under defined pharmacological conditions and following Hodgkin–Huxley formalism. Although in neuronal models, the membrane is usually considered  capacitance as a fixed parameter, the membrane ca-pacitance parameter is assumed as a control parameter to guarantee the existence of Hopf bifurcation using the Routh–Hurwitz criteria. The au-thors investigate the transition mechanism between the silent phase and tonic spiking mode. Furthermore, some simulations are provided using XPPAUT software for analytical results.


Main Subjects

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