Artículo
Saddle-node of limit cycles in planar piecewise linear systems and applications
Autor/es | Carmona Centeno, Victoriano
Fernández García, Soledad Teruel, Antonio E. |
Departamento | Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI) Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico |
Fecha de publicación | 2019-05 |
Fecha de depósito | 2024-01-31 |
Publicado en |
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Resumen | 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 ... 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. |
Agencias financiadoras | Ministerio de Economía y Competitividad through the project MTM2015-65608-P Junta de Andaucía by project P12-FQM-1658 University of Seville VPPI-US and partially supported by Ministerio de Economía y Competitividad through the project MTM2015-65608-P Junta de Andaucía by project P12-FQM-1658 |
Identificador del proyecto | MTM2015-65608-P
P12-FQM-1658 MTM2015-65608-P P12-FQM-1658 |
Cita | Carmona Centeno, V., Fernández García, S. y Teruel, A.E. (2019). Saddle-node of limit cycles in planar piecewise linear systems and applications. Discrete and Continuous Dynamical Systems, 39 (9), 5275-5299. https://doi.org/10.3934/dcds.2019215. |
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