LIMIT CYCLES AND INVARIANT CENTERS FOR AN EXTENDED KUKLES SYSTEM

被引：1
|
作者：
Liu, Zhenhai [1 ,2 ]
Szanto, Ivan [3 ]
机构：
[1] Guangxi Univ Nationalities, Guangxi Key Lab Univ Optimizat Control & Engn Cal, Nanning 530006, Guangxi, Peoples R China
[2] Guangxi Univ Nationalities, Coll Sci, Nanning 530006, Guangxi, Peoples R China
[3] Univ Tecn Federico Santa Maria, Dept Matemat, Casilla 110-5, Valparaiso, Chile
来源：
MISKOLC MATHEMATICAL NOTES | 2017年 / 18卷 / 02期
关键词：
limit cycle; center; bifurcation;
D O I：
10.18514/MMN.2017.2043
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
A class of polynomial systems of odd degree with limit cycles, invariant centers and invariant straight lines, is examined. The limit cycles can be obtain as a bifurcation of a non hyperbolic focus at the origin as Hopf bifurcations. We will also obtain the necessary and sufficient conditions for the critical point at the interior of bounded region to be a center.
引用
收藏
页码：947 / 952
页数：6
相关论文
共 50 条
  • [31] Limit cycles for a class of discontinuous piecewise generalized Kukles differential systems
    Mereu, Ana C.
    Oliveira, Regilene
    Rodrigues, Camila A. B.
    NONLINEAR DYNAMICS, 2018, 93 (04) : 2201 - 2212
  • [32] Limit cycles for extended bistable stochastic resonance system
    Zhang, XJ
    Wang, GX
    PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2004, 331 (3-4) : 467 - 476
  • [33] THE VARIATION OF INVARIANT LINES AND LIMIT CYCLES FOR A QUADRATIC DIFFERENTIAL SYSTEM
    叶惟寅
    Annals of Differential Equations, 1998, (02) : 286 - 293
  • [34] Limit Cycles and Isochronous Centers in a Class of Ninth Degree System
    Li Hongwei
    Li Feng
    Du Chaoxiong
    ABSTRACT AND APPLIED ANALYSIS, 2013,
  • [35] Multiple limit cycles and centers on center manifolds for Lorenz system
    Wang, Qinlong
    Huang, Wentao
    Feng, Jingjing
    APPLIED MATHEMATICS AND COMPUTATION, 2014, 238 : 281 - 288
  • [36] The isochronous centers for Kukles homogeneous system of degree nine
    Guo, Lina
    Liu, Changjian
    APPLIED MATHEMATICS LETTERS, 2021, 118
  • [37] Uniqueness of limit cycles for a class of cubic system with an invariant straight line
    Xie, Xiangdong
    Zhan, Qingyi
    NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2009, 70 (12) : 4217 - 4225
  • [38] On the Limit Cycles of a Class of Generalized Kukles Polynomial Differential Systems via Averaging Theory
    Makhlouf, Amar
    Menaceur, Amor
    INTERNATIONAL JOURNAL OF DIFFERENTIAL EQUATIONS, 2015, 2015
  • [39] NILPOTENT GLOBAL CENTERS OF GENERALIZED POLYNOMIAL KUKLES SYSTEM WITH DEGREE THREE
    Chen, Hebai
    Feng, Zhaosheng
    Zhang, Rui
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2024, 152 (09) : 3785 - 3800
  • [40] Limit cycles created by piecewise linear centers
    Llibre, Jaume
    Zhang, Xiang
    CHAOS, 2019, 29 (05)
12345