Fast-slow asymptotic for semi-analytical ignition criteria in FitzHugh-Nagumo system
Bezekci, B; Biktashev, VN
Date: 1 August 2017
Journal
Chaos: An Interdisciplinary Journal of Nonlinear Science
Publisher
AIP Publishing
Abstract
We study the problem of initiation of propagation of excitation waves in the FitzHugh-Nagumo model. Our approach is based on earlier works, based on the idea of approximating of the boundary between basins of attraction of propagating wave solutions and of decaying solutions as the stable manifold of the critical solution. Here, we ...
We study the problem of initiation of propagation of excitation waves in the FitzHugh-Nagumo model. Our approach is based on earlier works, based on the idea of approximating of the boundary between basins of attraction of propagating wave solutions and of decaying solutions as the stable manifold of the critical solution. Here, we obtain analytical expressions for the essential ingredients of the theory by singular perturbation using two small parameters, the separation of time scales of the activator and inhibitor, and the threshold in the activator's kinetics. This results in a closed analytical expression for the strength-duration curve.
Mathematics and Statistics
Faculty of Environment, Science and Economy
Item views 0
Full item downloads 0