We deal with the singularly perturbed Nagumo-type equation where ε > 0 is a real parameter and a : R -> R is a piecewise constant function satisfying 0 < a(s) < 1 for all s. For small ε, we prove the existence of chaotic, homoclinic and heteroclinic solutions. We use a dynamical systems approach, based on the Stretching Along Paths technique and on the Conley–Wazewski's method.
Asymptotic and chaotic solutions of a singularly perturbed Nagumo-type equation / Boscaggin, Alberto; Dambrosio, Walter; Papini, Duccio. - In: NONLINEARITY. - ISSN 0951-7715. - 28:10(2015), pp. 3465-3485. [10.1088/0951-7715/28/10/3465]
Asymptotic and chaotic solutions of a singularly perturbed Nagumo-type equation
PAPINI, Duccio
2015
Abstract
We deal with the singularly perturbed Nagumo-type equation where ε > 0 is a real parameter and a : R -> R is a piecewise constant function satisfying 0 < a(s) < 1 for all s. For small ε, we prove the existence of chaotic, homoclinic and heteroclinic solutions. We use a dynamical systems approach, based on the Stretching Along Paths technique and on the Conley–Wazewski's method.
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BosDamPap_Nonlinearity2015.pdf
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BoDaPa-Nonlinearity-postprint.pdf
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