Estabilidade assintótica global e continuação de soluções periódicas em sistemas suaves por partes com duas zonas no plano

Autor: Alexander Fernandes da Fonseca

Publikováno v: Biblioteca Digital de Teses e Dissertações da USPUniversidade de São PauloUSP.

Nesta tese estudamos um dos principais problemas na teoria qualitativa das equações diferenciais planares: o problema de determinar a bacia de atração de um ponto de equilíbrio. Damos uma prova rigorosa de que para sistemas lineares por partes d

Externí odkaz: http://www.teses.usp.br/teses/disponiveis/45/45132/tde-23082016-103753/

Limit cycles in planar piecewise linear Hamiltonian systems with three zones without equilibrium points

Autor: Jaume Llibre, Alexander Fernandes da Fonseca, Luis Fernando Mello

Publikováno v: Recercat: Dipósit de la Recerca de Catalunya
Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Recercat. Dipósit de la Recerca de Catalunya
instname
Dipòsit Digital de Documents de la UAB
Universitat Autònoma de Barcelona

We study the existence of limit cycles in planar piecewise linear Hamiltonian systems with three zones without equilibrium points. In this scenario, we have shown that such systems have at most one crossing limit cycle.

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9ff033422bee298c6c04e23a68f3638b
http://hdl.handle.net/2072/445043

Melnikov functions and limit cycles in piecewise smooth perturbations of a linear center using regularization method

Autor: Luis Fernando Mello, Denis de Carvalho Braga, Alexander Fernandes da Fonseca

Publikováno v: Nonlinear Analysis: Real World Applications. 36:101-114

In this article we study limit cycles in piecewise smooth perturbations of a linear center. In this setting it is common to adapt classical results for smooth systems, like Melnikov functions, to non-smooth ones. However, there is little justificatio

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::ecd8caa168d0e12835a7122d362da573
https://doi.org/10.1016/j.nonrwa.2017.01.003

The matching of two stable sewing linear systems in the plane

Autor: Alexander Fernandes da Fonseca, Denis de Carvalho Braga, Luis Fernando Mello

Publikováno v: Journal of Mathematical Analysis and Applications. 433:1142-1156

In this article we study one of the main problems in the qualitative theory of planar differential equations: the problem of determining the basin of attraction of an equilibrium point. We give a rigorous proof that for planar sewing piecewise linear

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::7dde9612311e9f22e78e29e453283de3
https://doi.org/10.1016/j.jmaa.2015.08.037