Stability and Hopf bifurcation in leech heart interneuron model

This article investigates the activity regimes of a realistic neuron model (as a slow-fast system). The authors study this model using the dynamical 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 capacitance parameter is assumed as a control parameter to guarantee the existence of Hopf bifurcation using the Routh–Hurwitz criteria. The authors investigate the transition mechanism between the silent phase and tonic spiking mode. Furthermore, some simulations are provided using XPPAUT software for analytical results.