The present monograph analyses the FitzHugh-Nagumo (F-N) model Le., the
Cauchy problem for some generalized Van der Pol equation depending on
three real parameters a, band c. This model, given in (1. 1. 17),
governs the initiation of the cardiac impulse. The presence of the three
parameters leads to a large variety of dy- namics, each of them
responsible for a specific functioning of the heart. For physiologists
it is highly desirable to have aglobai view of all possible
qualitatively distinct responses of the F-N model for all values of the
pa- rameters. This reduces to the knowledge of the global bifurcation
diagram. So far, only a few partial results appeared and they were
spread through- out the literature. Our work provides a more or less
complete theoretical and numerical investigation of the complex phase
dynamics and bifurca- tions associated with the F-N dynamical system.
This study includes the static and dynamic bifurcations generated by the
variation of a, band c and the corresponding oscillations, of special
interest for applications. It enables one to predict all possible types
of initiations of heart beats and the mechanism of transformation of
some types of oscillations into others by following the dynamics along
transient phase space trajectories. Of course, all these results hold
for the F-N model. The global phase space picture enables one to
determine the domain of validity of this model.
