Artículo
Saddle-node canard cycles in slow-fast planar piecewise linear differential systems
Autor/es | Carmona Centeno, Victoriano
Fernández García, Soledad Teruel Aguilar, Antonio Esteban |
Departamento | Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI) Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico |
Fecha de publicación | 2024-05 |
Fecha de depósito | 2024-02-19 |
Publicado en |
|
Resumen | By applying a singular perturbation approach, canard explosions exhibited by a general family of singularly perturbed planar Piecewise Linear (PWL) differential systems are analyzed. The performed study involves both ... By applying a singular perturbation approach, canard explosions exhibited by a general family of singularly perturbed planar Piecewise Linear (PWL) differential systems are analyzed. The performed study involves both hyperbolic and non-hyperbolic canard limit cycles appearing after both, a supercritical and a subcritical Hopf bifurcation. The obtained results are comparable with those obtained for smooth vector fields. In some sense, the manuscript can be understood as an extension towards the PWL framework of the results obtained for smooth systems by Dumortier and Roussarie in Mem. Am. Math. Soc. 1996, and Krupa and Szmolyan in J. Differ. Equ. 2001. In addition, some novel slow–fast behaviors are obtained. In particular, in the supercritical case, and under suitable conditions, it is proved that the limit cycles are organized along a curve exhibiting two folds. Each of these folds corresponds to a saddle–node bifurcation of canard limit cycles, one involving headless canard cycles, and the other involving canard cycles with head. This configuration also occurs in smooth systems with N-shaped fast nullcline. However, it has not been previously reported in the Van der Pol system. Our results provide justification for this observation. |
Agencias financiadoras | Junta de Andalucía (Consejería de Economía, Conocimiento, Empresas y Universidad) project TIC-0130 Junta de Andalucía (Consejería de Economía, Conocimiento, Empresas y Universidad) project P12-FQM-1658 Junta de Andalucía (Consejería de Economía, Conocimiento, Empresas y Universidad) project P20-01160 Junta de Andalucía (Consejería de Economía, Conocimiento, Empresas y Universidad) project US-1380740 Ministerio de Ciencia, Innovación y Universidades (MCIU), España project PGC2018-096265-B-I00 Ministerio de Ciencia, Innovación y Universidades (MCIU), España project PID2021- 123200NB-I00 Ministerio de Ciencia e Innovación, Spain through the project PID2021-123153OB-C21 |
Identificador del proyecto | TIC-0130
P12-FQM-1658 P20-01160 US-1380740 PGC2018-096265-B-I00 PID2021- 123200NB-I00 PID2021-123153OB-C21 |
Cita | Carmona Centeno, V., Fernández García, S. y Teruel Aguilar, A.E. (2024). Saddle-node canard cycles in slow-fast planar piecewise linear differential systems. Nonlinear Analysis: Hybrid Systems, 52 (101472). https://doi.org/10.1016/j.nahs.2024.101472. |
Ficheros | Tamaño | Formato | Ver | Descripción |
---|---|---|---|---|
NAHS_carmona-centeno_2024_sadd ... | 1.456Mb | [PDF] | Ver/ | |