A number of limit cycle of sextic polynomial differential systems via the averaging theory
Resumen
The main purpose of this paper is to study the number of limit cycles of sextic polynomial differential systems (SPDS) via the averaging theory which is an extension to the study of cubic polynomial vector fields in (Nonlinear Analysis 66 (2007), 1707--1721), where we provide an accurate upper bound of the maximum number of limit cycles that SPDS can have bifurcating from the period annulus surrounding the origin of a class of cubic system.
Descargas
Citas
Y. Bouattia, A. Makhlouf, Limit cycles of quartic and quintic polynomial differential systems via averaging theory, Ann. of Diff. Eqs.27, 1 (2011), 70-85.
A. Buica, J. Llibre, Averaging methods for finding periodic orbits vai Brouwer degree; Bulletin des Sciences mathematiques 128 (2004), 7-22.
B. Coll, A. Gasull, R.Prohens; Bifurcation of limit cycles from two families of centers, Dyn. Contin. Discrete Impuls. Syst. 12 (2005), 275–88.
L. Feng, W. Miao, Bifurcation of limit cycles in a quintic system with ten parameters; Nonlinear Dynam. 71 (2013), 213-222.
J. Gine, J. Llibre, Limit cycles of cubic polynomial vector fields via the averaging theory, Nonlinear Analysis 66 (2007), 1707–1721.
L. Hongwei, Limit cycles in a sextic Lyapunov system; Nonlinear Dynam. 72 (2013), 555-559.
J. Li, Hilbert’s 16th problem and bifurcations of planar polynomial vector elds, Int. J. Bifurcation and Chaos, 13 (2003), 47-106.
J. Lliber, A. Mereu; Limit cycles for generalized Kukles polynomial differential systems; Nonlinear Analysis 74 (2011), 1261-1271.
J. Llibre, R. M. Martins, M. A. Teixeira, Periodic orbits, invariant tori and cylinders of Hamiltonian systems near integrable ones having a return map equal to the identity; J. Math. Phys. 51 (2010), 082704.
S. Li, T. Huang, Limit cycles for piecewise smooth perturbations of a cubic polynomial differential center, Electronic Journal of Differential Equations, 108 (2015), 1-17.
L. S. Pontrjagin, Uber Autoschwingungssysteme, die den hamiltonshen nahe liegen, in: Physikalische Zeitschrift der Sowjetunion, Band 6, Heft (1–2), (1934), 25–28.
K. Xiaona, X. Yanqin, Limit cycle bifurcations in a class of quintic Z2-equivariant polynomial systems; Nonlinear Dynam. 73 (2013), 1271-1281.
Z. Yulin, Z. Huaiping; Bifurcation of limit cycles from a non-Hamiltonian quadratic integrable system with homoclinic loop; Infinite dimensional dynamical systems, 445-479, Fields Inst. Commun., 64, Springer, New York, 2013.
Derechos de autor 2020 Boletim da Sociedade Paranaense de Matemática
Esta obra está bajo licencia internacional Creative Commons Reconocimiento 4.0.
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).
