Geometry, integrability and bifurcation diagrams of a family of quadratic differential systems as application of the Darboux theory of integrability

Autor: Regilene Oliveira, Dana Schlomiuk, Ana Maria Travaglini, Claudia Valls

Publikováno v: Electronic Journal of Qualitative Theory of Differential Equations, Vol 2021, Iss 45, Pp 1-90 (2021)

During the last forty years the theory of integrability of Darboux, in terms of algebraic invariant curves of polynomial systems has been very much extended and it is now an active area of research. These developments are covered in numerous papers a

Externí odkaz: https://doaj.org/article/d6788e0583d143208fd37a64c012c87f

Global dynamics of the May-Leonard system with a Darboux invariant

Autor: Regilene Oliveira, Claudia Valls

Publikováno v: Electronic Journal of Differential Equations, Vol 2020, Iss 55,, Pp 1-19 (2020)

We study the global dynamics of the classic May-Leonard model in $\mathbb{R}^3$. Such model depends on two real parameters and its global dynamics is known when the system is completely integrable. Using the Poincare compactification on $\mathbb R

Externí odkaz: https://doaj.org/article/497279b376a44a2798dec9f1a1da47ba

Geometry, integrability and bifurcation diagrams of a family of quadratic differential systems as application of the Darboux theory of integrability

Autor: Claudia Valls, Regilene Oliveira, Dana Schlomiuk, Ana Maria Travaglini

Publikováno v: Electronic Journal of Qualitative Theory of Differential Equations, Vol 2021, Iss 45, Pp 1-90 (2021)
Repositório Institucional da USP (Biblioteca Digital da Produção Intelectual)
Universidade de São Paulo (USP)
instacron:USP

During the last forty years the theory of integrability of Darboux, in terms of algebraic invariant curves of polynomial systems has been very much extended and it is now an active area of research. These developments are covered in numerous papers a

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::cbea2a52910e3f45be38cce505b7fda3
https://doi.org/10.14232/ejqtde.2021.1.45

Limit cycles for two classes of control piecewise linear differential systems

Autor: Regilene Oliveira, Jaume Llibre, Camila Ap. B. Rodrigues

Publikováno v: Recercat. Dipósit de la Recerca de Catalunya
instname
Dipòsit Digital de Documents de la UAB
Universitat Autònoma de Barcelona
Recercat: Dipósit de la Recerca de Catalunya
Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
São Paulo Journal of Mathematical Sciences
Repositório Institucional da USP (Biblioteca Digital da Produção Intelectual)
Universidade de São Paulo (USP)
instacron:USP

We study the bifurcation of limit cycles from the periodic orbits of 2n–dimensional linear centers $${\dot{x}} = A_0 x$$ when they are perturbed inside classes of continuous and discontinuous piecewise linear differential systems of control theory

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1b0c0b9224d7ef2647ae745709fafadf
https://doi.org/10.1007/s40863-020-00163-7

On the limit cycle of a Belousov-Zhabotinsky differential systems

Autor: Jaume Llibre, Regilene Oliveira

Publikováno v: Repositório Institucional da USP (Biblioteca Digital da Produção Intelectual)
Universidade de São Paulo (USP)
instacron:USP
Dipòsit Digital de Documents de la UAB
Universitat Autònoma de Barcelona

In Leonov and Kuznetsov (2013), the authors shown numerically the existence of a limit cycle surrounding the unstable node that system (1) has in the positive quadrant for specific values of the parameters. System (1) is one of the Belousov-Zhabotins

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::51503d9f6ef3ab14f37ac6f4dc47f431