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HOMOCLINIC ORBITS OF THE FITZHUGH-NAGUMO EQUATION: THE SINGULAR-LIMIT
FITZHUGH-NAGUMO EQUATION SINGULAR-LIMIT
2015/8/25
The FitzHugh-Nagumo equation has been investigated with a wide
array of different methods in the last three decades. Recently a version of
the equations with an applied current was analyzed by Champ...
Homoclinic Orbits of the FitzHugh–Nagumo Equation: Bifurcations in the Full System
homoclinic bifurcation singular perturbation
2015/8/25
This paper investigates travelling wave solutions of the FitzHugh–Nagumo equation from the viewpoint
of fast-slow dynamical systems. These solutions are homoclinic orbits of a three dimensional
vect...
Exponential Dichotomies and Homoclinic Orbits from Heteroclinic Cycles
Exponential Dichotomies Homoclinic Orbits Heteroclinic Cycle Melnikov Function
2013/1/30
In this paper, we investigate the homoclinic bifurcations from a heteroclinic cycle by using exponential dichotomies.We give a Melnikov!atype condition assuring the existence ofhomoclinic orbits form ...
Normally Elliptic Singular Perturbations and Persistence of Homoclinic Orbits
Normally Elliptic Singular Perturbations Persistence of Homoclinic Orbits
2011/1/14
We consider a dynamical system, possibly infinite dimensional or non-autonomous, with fast and slow time scales which is oscillatory with high frequencies in the fast directions. We first derive and j...
Analytic and algebraic conditions for bifurcations of homoclinic orbits I: Saddle equilibria
Homoclinic orbit bifurcation Differential Galois theory Melnikov method
2010/11/30
We study bifurcations of homoclinic orbits to hyperbolic saddle equilibria in a class of four-dimensional systems which may be Hamil-tonian or not. Only one parameter is enough to treat these types of...