Pacemaker dynamics in the full Morris–Lecar model

• The pacemaker dynamics of an experimentally founded model of a muscle cell is studied using bifurcation theory.
• The model is found to be capable of displaying sustained oscillations in the absence of electrical stimulation.
• The existence of oscillatory dynamics is associated to the strength of a leak current.
• Spontaneous oscillations are shown to be generated by Hopf bifurcations.
• Suppression of the oscillations is associated to the interaction of fold and Hopf bifurcations.

This article reports the finding of pacemaker dynamics in certain region of the parameter space of the three-dimensional version of the Morris–Lecar model for the voltage oscillations of a muscle cell. This means that the cell membrane potential displays sustained oscillations in the absence of an external electrical stimulation. The development of this dynamic behavior is shown to be tied to the strength of the leak current contained in the model. The approach followed is mostly based on the use of linear stability analysis and numerical continuation techniques. In this way it is shown that the oscillatory dynamics is associated to the existence of two Hopf bifurcations, one subcritical and other supercritical. Moreover, it is explained that in the region of parameter values most commonly studied for this model such pacemaker dynamics is not displayed because of the development of two fold bifurcations, with the increase of the strength of the leak current, whose interaction with the Hopf bifurcations destroys the oscillatory dynamics.