Stability of pulse solutions for the discrete FitzHugh–Nagumo system
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Abstract:
We show that the fast travelling pulses of the discrete FitzHugh–Nagumo system in the weak-recovery regime are nonlinearly stable. The spectral conditions that need to be verified involve linear operators that are associated to functional differential equations of mixed type. Such equations are ill-posed and do not admit a semi-flow, which precludes the use of standard Evans-function techniques. Instead, we construct the potential eigenfunctions directly by using exponential dichotomies, Fredholm techniques and an infinite-dimensional version of the Exchange Lemma.References
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Additional Information
- H. J. Hupkes
- Affiliation: Division of Applied Mathematics, Brown University, 182 George Street, Providence, Rhode Island 02912
- Address at time of publication: Mathematisch Instituut, Universiteit Leiden, P.O. Box 9512, 2300 RA Leiden, The Netherlands
- MR Author ID: 768528
- Email: hjhupkes@dam.brown.edu, hhupkes@math.leidenuniv.nl
- B. Sandstede
- Affiliation: Division of Applied Mathematics, Brown University, 182 George Street, Providence, Rhode Island 02912
- ORCID: 0000-0002-5432-1235
- Email: bjorn_sandstede@brown.edu
- Received by editor(s): May 6, 2010
- Received by editor(s) in revised form: February 1, 2011
- Published electronically: July 11, 2012
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 365 (2013), 251-301
- MSC (2010): Primary 34A33, 34K26, 34D35, 34K08
- DOI: https://doi.org/10.1090/S0002-9947-2012-05567-X
- MathSciNet review: 2984059