Global bifurcation structure of a Bonhoeffer-van der Pol oscillator driven by periodic pulse trains: Comparison with data from a periodically inhibited biological pacemaker

The Bonhoeffer-van der Pol (BVP) oscillator is a valuable dynamical system model of pacemaker neurons. Isochrons, phase transition curves (PTC), and two dimensional bifurcation diagrams served to analyze the neuron's response to periodic pulse stimuli. Responses are described and explained in terms of the nonlinear dynamical system theory. An important issue in the generation of spikes by pacemaker neurons is the existence of both slow and fast dynamics in the state point's trajectory in the phase plane. It is this feature in particular that makes the BVP oscillator a faithful model of living pacemaker neurons. Comparison of the model's responses with those of a living pacemaker was based also on return maps of interspike intervals. Analyzed in detail were the complex discharges called 'stammering' which involve interspike intervals that arise unpredictably and exhibit histograms with several modes separated by the equal intervals.