WIAS Preprint No. 213, (1996)

Stability of N-fronts bifurcating from a twisted heteroclinic loop and an application to the FitzHugh-Nagumo equation



Authors

  • Sandstede, Björn

2010 Mathematics Subject Classification

  • 34C37 35B35 58F14

Keywords

  • Heteroclinic orbits, Stability, FitzHugh-Nagumo equation

Abstract

In this article existence and stability of N-front travelling wave solutions of partial differential equations on the real line is investigated. The N-fronts considered here arise as heteroclinic orbits bifurcating from a twisted heteroclinic loop in the underlying ordinary differential equation describing travelling wave solutions. It is proved that the N-front solutions are linearly stable provided the fronts building the twisted heteroclinic loop are linearly stable. The result is applied to travelling waves arising in the FitzHugh-Nagumo equation.

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