https://doi.org/10.1140/epjp/i2011-11017-9
Regular Article
Spike transitions in the FitzHugh-Nagumo model
Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133, Milano, Italy
* e-mail: paolo.biscari@polimi.it
Received:
21
January
2011
Accepted:
7
February
2011
Published online:
16
February
2011
The FitzHugh-Nagumo nonlinear dynamical system has been thoroughly studied in the last decades. Its capability of reproducing crucial features of the dynamics of complex systems has suggested applications in the study of both the neuronal activity and the cardiodynamics. In the phase plane, the variation of the constitutive parameters may induce Hopf bifurcations which modify the number and the stability of equilibrium configurations. Moreover, orbits evolving towards a stable equilibrium configuration may exhibit one or more spikes during their evolution. The present study aims at introducing a classification of the trajectories in the phase plane on the basis of the number of spikes evidenced by the action potential. We analyze a wide range of values of the relevant physiological parameters, and identify the critical values which induce different macroscopic behaviors.
PACS: 87.19.Hh Cardiac dynamics – / 87.10.Ed Ordinary differential equations (ODE), partial differential equations (PDE), integrodifferential models –
© Società Italiana di Fisica and Springer, 2011
