Published January 31, 2024
| Version v1
Publication
Saddle-node of limit cycles in planar piecewise linear systems and applications
Contributors
Others:
- Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI)
- Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico
- Universidad de Sevilla. TIC130: Investigación en Sistemas Dinámicos en Ingeniería
- Universidad de Sevilla. FQM120: Modelado Matemático y Simulación de Sistemas Medioambientales
- 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
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.
Additional details
Identifiers
- URL
- https://idus.us.es/handle//11441/154287
- URN
- urn:oai:idus.us.es:11441/154287
Origin repository
- Origin repository
- USE