Saddle-node canard cycles in slow-fast planar piecewise linear differential systems

Show simple item record Carmona, V. Fernández-García, S. Teruel, A.E. 2024-02-12T08:59:16Z
dc.description.abstract 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 com- parable 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.
dc.format application/pdf
dc.relation.isformatof Versió postprint del document publicat a:
dc.relation.ispartof Nonlinear Analysis-Hybrid Systems, 2024
dc.subject.classification 51 - Matemàtiques
dc.subject.classification 004 - Informàtica
dc.subject.other 51 - Mathematics
dc.subject.other 004 - Computer Science and Technology. Computing. Data processing
dc.title Saddle-node canard cycles in slow-fast planar piecewise linear differential systems
dc.type info:eu-repo/semantics/article
dc.type info:eu-repo/semantics/acceptedVersion 2024-02-12T08:59:17Z info:eu-repo/date/embargoEnd/2026-05-01
dc.embargo 2026-05-01
dc.subject.keywords Piecewise linear differential systems
dc.subject.keywords Bifurcations
dc.subject.keywords slow-fast dynamics
dc.subject.keywords canard orbits
dc.subject.keywords saddle-node canard orbits
dc.rights.accessRights info:eu-repo/semantics/embargoedAccess

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