Local codimension-1 bifurcations in planar Filippov systems
This thesis serves as an introduction to the qualitative theory of non-smooth dynamics, particularly focusing on codimension-1 bifurcations in planar systems. It includes a review of canonical forms for codimension-1 vector fields as well as the proof of their existence, a demonstration of the exist...
| Autor: | |
|---|---|
| Tipo de recurso: | tesis de maestría |
| Fecha de publicación: | 2024 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/415263 |
| Acceso en línea: | https://hdl.handle.net/2117/415263 |
| Access Level: | acceso abierto |
| Palabra clave: | Differentiable dynamical systems Non-smooth dynamics bifurcations canonical forms pseudo-Hopf. Sistemes dinàmics diferenciables Classificació AMS::37 Dynamical systems and ergodic theory::37N Applications Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Sistemes dinàmics |
| Sumario: | This thesis serves as an introduction to the qualitative theory of non-smooth dynamics, particularly focusing on codimension-1 bifurcations in planar systems. It includes a review of canonical forms for codimension-1 vector fields as well as the proof of their existence, a demonstration of the existence of the hyperbolic limit cycle in the invisible fold-fold for $\alpha>0$, and a comparative study of the invisible fold-fold bifurcation with the classical Andronov-Hopf bifurcation. In the assessment of the limit cycle's stability, it is been adapted a method from classical dynamical systems developed in \cite{andronov1971theory}. |
|---|