Dynamics of the FitzHugh-Nagumo system having invariant algebraic surfaces
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Tian, Yuzhou (Sun Yat-sen University. School of Mathematics (China))

Date:	2021
Abstract:	In this paper, we study the dynamics of the FitzHugh-Nagumo system x˙=z,y˙=b(x-dy),z˙=x(x-1)(x-a)+y+cz having invariant algebraic surfaces. This system has four different types of invariant algebraic surfaces. The dynamics of the FitzHugh-Nagumo system having two of these classes of invariant algebraic surfaces have been characterized in Valls (J Nonlinear Math Phys 26:569-578, 2019). Using the quasi-homogeneous directional blow-up and the Poincaré compactification, we describe the dynamics of the FitzHugh-Nagumo system having the two remaining classes of invariant algebraic surfaces. Moreover, for these FitzHugh-Nagumo systems we prove that they do not have limit cycles.
Grants:	Ministerio de Ciencia e Innovación MTM2016-77278-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1617 European Commission 777911
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Global dynamics ; FitzHugh-Nagumo system ; Invariant algebraic surface ; Poincaré compactification
Published in:	Zeitschrift fur Angewandte Mathematik und Physik, Vol. 72, Issue 1 (February 2021) , art. 15, ISSN 0044-2275

DOI: 10.1007/s00033-020-01450-1

Postprint 16 p, 793.8 KB

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