Limit cycles for discontinuous generalized Lienard polynomial differential equations

Autor: Jaume Llibre, Ana Cristina Mereu

Publikováno v: Electronic Journal of Differential Equations, Vol 2013, Iss 195,, Pp 1-8 (2013)

We divide $\mathbb{R}^2$ into sectors $S_1,\dots ,S_l$, with $l>1$ even, and define a discontinuous differential system such that in each sector, we have a smooth generalized Lienard polynomial differential equation $\ddot{x}+f_i(x)\dot{x} +g_i(x)

Externí odkaz: https://doaj.org/article/75a316ec9fd14eb788d5c4fe43e83e4e

Zero-Hopf bifurcation in a 3-D jerk system

Autor: Ana Cristina Mereu, Francisco Braun

Let the three-dimensional differential system defined by the jerk equation x = − a x + x x 2 − x 3 − b x + c x , with a , b , c ∈ R . When a = b = 0 and c 0 the equilibrium point localized at the origin of coordinates is a zero-Hopf equilibri

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a2444b01460688c64a3702bee2287ef1
http://arxiv.org/abs/2003.12280

Limit cycles in uniform isochronous centers of discontinuous differential systems with four zones

Autor: Regilene Oliveira, Jackson Itikawa, Jaume Llibre, Ana Cristina Mereu

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

We apply the averaging theory of first order for discontinuous differential systems to study the bifurcation of limit cycles from the periodic orbits of the uniform isochronous center of the differential systems \begin{document} $\dot{x}=-y+x^2, \;\d

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::55e028dc97a913d9953ccb965cc28845
https://ddd.uab.cat/record/221378

Reversibility and branching of periodic orbits

Autor: Marco Antonio Teixeira, Ana Cristina Mereu

Publikováno v: Discrete & Continuous Dynamical Systems - A. 33:1177-1199

We study the dynamics near an equilibrium point of a $2$-parameter family of a reversible system in $\mathbb{R}^6$. In particular, we exhibit conditions for the existence of periodic orbits near the equilibrium of systems having the form $x^{(vi)}+ \

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::21c16c23e4b23cf84c64f19c596450a6
https://doi.org/10.3934/dcds.2013.33.1177

Limit cycles for generalized Kukles polynomial differential systems

Autor: Jaume Llibre, Ana Cristina Mereu

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

We study the limit cycles of generalized Kukles polynomial differential systems using averaging theory of first and second order.

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::654027347a9d315a7540c1301fb69b99
https://doi.org/10.1016/j.na.2010.09.064