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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...
Periodic and homoclinic orbits in a toy climate model
Periodic and homoclinic orbits toy climate model
2009/11/16
A two dimensional system of autonomous nonlinear ordinary differential equations models glacier growth and temperature changes on an idealized planet. We apply standard perturbative techniques from dy...
BIFURCATIONS FROM HOMOCLINIC ORBITS FOR SECOND ORDER HAMILTONIAN SYSTEM
Bifurcations homoclinic orbit Hamilton
2007/8/7
An existence theorem of homoclinic orbit is given for second order Hamiltonian system -\"{x}(t) + a(t)x(t) - W_x(t, x(t)) = \lambda x(t) when \lambda=\lambda_1, where \lambda_1 is the first eigenvalue...