Universal aspects of light halo nuclei

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Effective Fokker-Planck equation for birhythmic modified van der Pol oscillator

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A singular approach to discontinuous vector fields on the plane

In this paper we deal with discontinuous vector fields on R-2 and we prove that the analysis of their local behavior around a typical singularity can be treated via singular perturbation. The regularization process developed by Sotomayor and Teixeira is crucial for the development of this work. (c) 2006 Elsevier B.V. All rights reserved.

3-Dimensional hopf bifurcation via averaging theory

We consider the Lorenz system ẋ = σ(y - x), ẏ = rx - y - xz and ż = -bz + xy; and the Rössler system ẋ = -(y + z), ẏ = x + ay and ż = b - cz + xz. Here, we study the Hopf bifurcation which takes place at q± = (±√br - b,±√br - b, r - 1), in the Lorenz case, and at s± = (c+√c2-4ab/2, -c+√c2-4ab/2a, c±√c2-4ab/2a) in the Rössler case. As usual this Hopf bifurcation is in the sense that an one-parameter family in ε of limit cycles bifurcates from the singular point when ε = 0. Moreover, we can determine the kind of stability of these limit cycles. In fact, for both systems we can prove that all the bifurcated limit cycles in a neighborhood of the singular point are either a local attractor, or a local repeller, or they have two invariant manifolds, one stable and the other unstable, which locally are formed by two 2-dimensional cylinders. These results are proved using averaging theory. The method of studying the Hopf bifurcation using the averaging theory is relatively general and can be applied to other 3- or n-dimensional differential systems.

Closed poly-trajectories and Poincaré index of non-smooth vector fields on the plane

This paper is concerned with closed orbits of non-smooth vector fields on the plane. For a class of non-smooth vector fields we provide necessary and sufficient conditions for the existence of closed poly-trajectorie. By means of a regularization process we prove that hyperbolic closed poly-trajectories are limit sets of a sequence of limit cycles of smooth vector fields. In our approach the Poincaré Index for non-smooth vector fields is introduced. © 2013 Springer Science+Business Media New York.

Piecewise linear perturbations of a linear center

This paper is mainly devoted to the study of the limit cycles that can bifurcate from a linear center using a piecewise linear perturbation in two zones. We consider the case when the two zones are separated by a straight line Σ and the singular point of the unperturbed system is in Σ. It is proved that the maximum number of limit cycles that can appear up to a seventh order perturbation is three. Moreover this upper bound is reached. This result confirms that these systems have more limit cycles than it was expected. Finally, center and isochronicity problems are also studied in systems which include a first order perturbation. For the latter systems it is also proved that, when the period function, defined in the period annulus of the center, is not monotone, then it has at most one critical period. Moreover this upper bound is also reached.

Ciclos limites de sistemas lineares por partes

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Estudo de ciclos limites em sistemas diferenciais lineares por partes

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

O método do Avering via teoria do grau de Brouwer e aplicações

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Bifurcações em sistemas dinâmicos suaves por partes

Pós-graduação em Matemática - IBILCE

Ciclos limites e a equação de van der Pol

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Ciclos limites de campos de vetores polinomiais cúbicos e quadráticos

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

O método averagin e aplicações

Pós-graduação em Matemática - IBILCE

Conjuntos limite e bifurfações de campos de vetores suaves por partes no plano

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Equações com impasse e problemas de perturbação singular

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)