Stability of pulse solutions for the discrete FitzHugh–Nagumo system

Hupkes, H.; Sandstede, B.

doi:10.1090/S0002-9947-2012-05567-X

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ISSN 1088-6850(online) ISSN 0002-9947(print)

Stability of pulse solutions for the discrete FitzHugh-Nagumo system

Authors: H. J. Hupkes and B. Sandstede
Journal: Trans. Amer. Math. Soc. 365 (2013), 251-301
MSC (2010): Primary 34A33, 34K26, 34D35, 34K08
Posted: July 11, 2012
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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.

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