Dynamics of the FitzHugh-Nagumo system having invariant algebraic surfaces
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 algebr...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2021 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:236667 |
| Acceso en línea: | https://ddd.uab.cat/record/236667 https://dx.doi.org/urn:doi:10.1007/s00033-020-01450-1 |
| Access Level: | acceso abierto |
| Palabra clave: | Global dynamics FitzHugh-Nagumo system Invariant algebraic surface Poincaré compactification |
| Sumario: | 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. |
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