TL;DR
This paper analyzes the initial value problem for the FitzHugh-Nagumo equations, providing explicit solutions under piecewise linear approximations and exploring wave propagation, with implications for nonlinear cases.
Contribution
It offers explicit solutions for the initial value problem and evaluates wave speeds in the FitzHugh-Nagumo model using piecewise linear approximations.
Findings
Explicit solutions for the initial value problem are derived.
Damped traveling waves and their speeds are characterized.
Results extend to nonlinear cases.
Abstract
The initial value problem P0, in all of the space, for the spatio - temporal FitzHugh - Nagumo equations is analyzed. When the reaction kinetics of the model can be outlined by means of piecewise linear approximations, then the solution of P0 is explicitly obtained. For periodic initial data are possible damped travelling waves and their speed of propagation is evaluated. The results imply applications also to the non linear case.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.