A cubic system with a limit cycle bounded by two invariant parabolas

被引：1
|
作者：
Sáez E. [1 ]
Szántó I. [1 ]
机构：
[1] Departamento de Matemática, Universidad Técnica Federico Santa María, Valparaíso
来源：
Differential Equations and Dynamical Systems | 2009年 / 17卷 / 1-2期
关键词：
Center; Invariant algebraic curves; Limit cycles; Polynomial differential equations;
D O I：
10.1007/s12591-009-0012-z
中图分类号：
学科分类号：
摘要：
We show the existence of a cubic system having at least one limit cycle bounded by two invariant parabolas. We will also obtain the necessary and sufficient conditions for the critical point in the interior of the bounded region to be a center. © 2009 Foundation for Scientific Research and Technological Innovation.
引用
收藏
页码：163 / 168
页数：5
相关论文
共 50 条
  • [21] The Problem of the Centre for Cubic Systems with Two Parallel Invariant Straight Lines and One Invariant Conic
    Cozma, Dumitru
    NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2009, 16 (02): : 213 - 234
  • [22] LIMIT CYCLES AND INVARIANT CENTERS FOR AN EXTENDED KUKLES SYSTEM
    Liu, Zhenhai
    Szanto, Ivan
    MISKOLC MATHEMATICAL NOTES, 2017, 18 (02) : 947 - 952
  • [23] Limit Cycle stability of two degree of freedom system under deterministic and random perturbation
    Naprstek, J.
    Fischer, C.
    EURODYN 2014: IX INTERNATIONAL CONFERENCE ON STRUCTURAL DYNAMICS, 2014, : 1943 - 1956
  • [24] Invariant algebraic curves for the cubic Lienard system with linear damping
    Chavarriga, J.
    Garcia, I. A.
    Llibre, J.
    Zoladek, H.
    BULLETIN DES SCIENCES MATHEMATIQUES, 2006, 130 (05): : 428 - 441
  • [25] Stability of Time-Invariant Extremum Seeking Control for Limit Cycle Minimization
    Kumar, Saurav
    Makarenkov, Oleg
    Gregg, Robert D.
    Gans, Nicholas
    IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2022, 67 (09) : 5017 - 5024
  • [26] THE PROBLEM OF THE CENTRE FOR CUBIC DIFFERENTIAL SYSTEMS WITH TWO HOMOGENEOUS INVARIANT STRAIGHT LINES AND ONE INVARIANT CONIC
    Dumitru Cozma
    Annals of Applied Mathematics, 2010, (04) : 385 - 399
  • [27] Limit cycles in a cubic predator-prey differential system
    Huang, Xuncheng
    Wang, Yuanming
    Cheng, Ansheng
    JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, 2006, 43 (04) : 829 - 843
  • [28] LIMIT CYCLE BIFURCATIONS FROM CENTERS OF SYMMETRIC HAMILTONIAN SYSTEMS PERTURBED BY CUBIC POLYNOMIALS
    Hu, Zhaoping
    Gao, Bin
    Romanovski, Valery G.
    INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2013, 23 (03):
  • [29] The center conditions and bifurcation of limit cycles at the infinity for a cubic polynomial system
    Zhang, Lina
    Liu, Yirong
    Jiang, Xuejiao
    APPLIED MATHEMATICS AND COMPUTATION, 2011, 218 (04) : 1360 - 1370
  • [30] A CUBIC SYSTEM WITH 8 SMALL-AMPLITUDE LIMIT-CYCLES
    NING, SC
    MA, SL
    KWEK, KH
    ZHENG, ZM
    APPLIED MATHEMATICS LETTERS, 1994, 7 (04) : 23 - 27
12345