Saddle-node of limit cycles in planar piecewise linear systems and applications
In this article, we prove the existence of a saddle-node bifurcation of limit cycles in continuous piecewise linear systems with three zones. The bifurcation arises from the perturbation of a non-generic situation, where there exists a linear center in the middle zone. We obtain an approximation of...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2019 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/154287 |
| Acceso en línea: | https://hdl.handle.net/11441/154287 https://doi.org/10.3934/dcds.2019215 |
| Access Level: | acceso abierto |
| Palabra clave: | Piecewise linear systems Bifurcations Saddle-node of limit cycles Neuroscience |
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oai:idus.us.es:11441/154287 |
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España |
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Saddle-node of limit cycles in planar piecewise linear systems and applications Carmona Centeno, Victoriano Fernández García, Soledad Teruel, Antonio E. Piecewise linear systems Bifurcations Saddle-node of limit cycles Neuroscience In this article, we prove the existence of a saddle-node bifurcation of limit cycles in continuous piecewise linear systems with three zones. The bifurcation arises from the perturbation of a non-generic situation, where there exists a linear center in the middle zone. We obtain an approximation of the relation between the parameters of the system, such that the saddle-node bifurcation takes place, as well as of the period and amplitude of the non-hyperbolic limit cycle that bifurcates. We consider two applications, first a piecewise linear version of the FitzHugh-Nagumo neuron model of spike generation and second an electronic circuit, the memristor oscillator. American Institute of Mathematical Sciences (AIMS) https://hdl.handle.net/11441/154287 https://doi.org/10.3934/dcds.2019215 |
| title |
Saddle-node of limit cycles in planar piecewise linear systems and applications |
| spellingShingle |
Saddle-node of limit cycles in planar piecewise linear systems and applications Carmona Centeno, Victoriano Piecewise linear systems Bifurcations Saddle-node of limit cycles Neuroscience |
| title_short |
Saddle-node of limit cycles in planar piecewise linear systems and applications |
| title_full |
Saddle-node of limit cycles in planar piecewise linear systems and applications |
| title_fullStr |
Saddle-node of limit cycles in planar piecewise linear systems and applications |
| title_full_unstemmed |
Saddle-node of limit cycles in planar piecewise linear systems and applications |
| title_sort |
Saddle-node of limit cycles in planar piecewise linear systems and applications |
| author |
Carmona Centeno, Victoriano |
| author_facet |
Carmona Centeno, Victoriano Fernández García, Soledad Teruel, Antonio E. |
| author_role |
author |
| author2 |
Fernández García, Soledad Teruel, Antonio E. |
| author2_role |
author author |
| topic |
Piecewise linear systems Bifurcations Saddle-node of limit cycles Neuroscience |
| topic_facet |
Piecewise linear systems Bifurcations Saddle-node of limit cycles Neuroscience |
| description |
In this article, we prove the existence of a saddle-node bifurcation of limit cycles in continuous piecewise linear systems with three zones. The bifurcation arises from the perturbation of a non-generic situation, where there exists a linear center in the middle zone. We obtain an approximation of the relation between the parameters of the system, such that the saddle-node bifurcation takes place, as well as of the period and amplitude of the non-hyperbolic limit cycle that bifurcates. We consider two applications, first a piecewise linear version of the FitzHugh-Nagumo neuron model of spike generation and second an electronic circuit, the memristor oscillator. |
| publishDate |
2019 |
| format |
article |
| status_str |
publishedVersion |
| url |
https://hdl.handle.net/11441/154287 https://doi.org/10.3934/dcds.2019215 |
| eu_rights_str_mv |
openAccess |
| publisher |
American Institute of Mathematical Sciences (AIMS) |
| institution |
Universidad de Sevilla (US) |
| collection |
idUS. Depósito de Investigación de la Universidad de Sevilla |
| reponame_str |
idUS. Depósito de Investigación de la Universidad de Sevilla |
| instname_str |
Universidad de Sevilla (US) |
| _version_ |
1878440963546808320 |
| publishDateSort |
2019 |
| author_browse |
Carmona Centeno, Victoriano Fernández García, Soledad Teruel, Antonio E. |
| publisherStr |
American Institute of Mathematical Sciences (AIMS) |
| score |
6,9303427 |