Dynamics of the FitzHugh-Nagumo system having invariant algebraic surfaces
type: Item
instance of: scholarly article
title: Dynamics of the FitzHugh-Nagumo system having invariant algebraic surfaces
zbMATH Open document ID: 1476.37032
author: Jaume Llibre
author: Yuzhou Tian
published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik
publication date: 2021-05-19T00:00:00Z
review text: The purpose of this study is to classify the dynamics of the FitzHugh-Nagumo system \[\dot{x}=z, \quad \dot{y}=b(x-dy), \quad \dot{z}=x(x-1)(x-a)+y+cz\] having invariant algebraic surfaces. The 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 has been studied in [\textit{C. Valls}, J. Nonlinear Math. Phys. 26, No. 4, 569--578 (2019; Zbl 1418.34072)]. Applying the quasi-homogeneous directional blow-up and the Poincaré compactification, the authors describe the dynamics of the FitzHugh-Nagumo system having the two remaining classes of invariant algebraic surfaces. Moreover, it is proved that these FitzHugh-Nagumo systems have no limit cycles.
reviewed by: Alexander Grin
Mathematics Subject Classification ID: 37C10
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 34C07
Mathematics Subject Classification ID: 37C79
zbMATH DE Number: 7349782
zbMATH Keywords: global dynamics
zbMATH Keywords: FitzHugh-Nagumo system
zbMATH Keywords: invariant algebraic surface
zbMATH Keywords: Poincaré compactification
MaRDI profile type: Publication
full work available at URL: s00033-020-01450-1
OpenAlex ID: W3120317866
cites work: A SURVEY ON THE BLOW UP TECHNIQUE
cites work: Existence and stability of traveling pulse solutions of the FitzHugh-Nagumo equation
cites work: Q3994902
cites work: Topological equivalence of a plane vector field with its principal part defined through Newton polyhedra
cites work: Bounded Polynomial Vector Fields
cites work: Q4280766
cites work: Qualitative theory of planar differential systems
cites work: Stability Analysis for the Slow Travelling Pulse of the FitzHugh–Nagumo System
cites work: Q3254327
cites work: Existence of wavefronts and impulses to FitzHugh-Nagumo equations
cites work: Stability of pulse solutions for the discrete FitzHugh–Nagumo system
cites work: Stability of the Travelling Wave Solution of the Fitzhugh-Nagumo System
cites work: Turning points and traveling waves in Fitzhugh--Nagumo type equations
cites work: GLOBAL DYNAMICS OF THE LORENZ SYSTEM WITH INVARIANT ALGEBRAIC SURFACES
cites work: Quadratic systems with invariant straight lines of total multiplicity two having Darboux invariants
cites work: Analytic first integrals of the FitzHugh-Nagumo systems
cites work: Liouvillian integrability of the FitzHugh-Nagumo systems
cites work: Classification of Continuous Flows on 2-Manifolds
cites work: On the global dynamics of the Newell–Whitehead system
cites work: Invariant algebraic surfaces of the FitzHugh-Nagumo system
DOI: 10.1007/S00033-020-01450-1
description: scientific article; zbMATH DE number 7349782