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| Author(s): |
Kamila da Silva Andrade
Total Authors: 1
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| Document type: | Doctoral Thesis |
| Press: | Campinas, SP. |
| Institution: | Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica |
| Defense date: | 2016-03-31 |
| Examining board members: |
Marco Antonio Teixeira;
Ana Cristina de Oliveira Mereu;
Regilene Delazari dos Santos Oliveira;
João Carlos da Rocha Medrado;
Luis Fernando de Osorio Mello
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| Advisor: | Marco Antonio Teixeira; Mike R Jeffrey; Ricardo Miranda Martins |
| Abstract | |
In this work, a study is performed on cycles occurring typically in planar discontinuous vector fields in two zones, Z=(X,Y), with switching manifold being the inverse image of 0 by a smooth function h, defined on the plane and assuming real values, for which 0 is a regular value. Firstly, it is shown that if X and Y are analytic vector fields and C is a polycycle of Z, then, generically, C cannot have limit cycles accumulating onto it. After that, the objective is to study the bifurcations of typical cycles through a saddle-regular point. More specifically, we consider a cycle composed by one segment of a regular orbit of Z, which crosses the switching manifold transversally, and a saddle-regular point, resulting in a homoclinic-like connection. Bifurcation diagrams are presented for the case where the hyperbolicity ratio of the saddle point is a irrational number, the case where hyperbolicity ratio is a rational number is illustrated with models. Finally, two application models presenting cycles through saddle-regular points are studied by means of numeric calculations (AU) | |
| FAPESP's process: | 13/07523-9 - Bifurcations of Degenerated Cycles in Discontinuous Systems |
| Grantee: | Kamila da Silva Andrade |
| Support Opportunities: | Scholarships in Brazil - Doctorate |