INTEGRABILITY AND BIFURCATIONS OF LIMIT CYCLES IN A CUBIC KOLMOGOROV SYSTEM

被引：6
|
作者：
Feng, Li [1 ]
机构：
[1] Linyi Univ, Sch Sci, Linyi, Shandong, Peoples R China
来源：
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2013年 / 23卷 / 04期
关键词：
Kolmogorov systems; center-focus problem; Lyapunov constant; limit circle;
D O I：
10.1142/S0218127413500612
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We investigate the planar cubic Kolmogorov systems with three invariant algebraic curves which have a equilibrium at (1, 1). With the help of computer algebra system MATHEMATICA, we prove that five limit cycles can be bifurcated from a critical point in the first quadrant. Moreover, the necessary conditions of center are obtained, by technical transformation, and its sufficiencies are proved.
引用
收藏
页数：6
相关论文
共 50 条
  • [11] Bifurcations of limit cycles for a cubic Hamiltonian system under quartic perturbations
    Zhang, TH
    Han, MA
    Zang, H
    Meng, XZ
    CHAOS SOLITONS & FRACTALS, 2004, 22 (05) : 1127 - 1138
  • [12] BIFURCATIONS OF LIMIT CYCLES AND CENTER PROBLEM FOR A CLASS OF CUBIC NILPOTENT SYSTEM
    Liu, Yirong
    Li, Jibin
    INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2010, 20 (08): : 2579 - 2584
  • [13] BIFURCATIONS OF LIMIT-CYCLES FORMING COMPOUND EYES IN THE CUBIC SYSTEM
    LI, JB
    HUANG, QM
    CHINESE ANNALS OF MATHEMATICS SERIES B, 1987, 8 (04) : 391 - 403
  • [14] Nondegenerate centers and limit cycles of cubic Kolmogorov systems
    Antonio Algaba
    Cristóbal García
    Jaume Giné
    Nonlinear Dynamics, 2018, 91 : 487 - 496
  • [15] Multiple stable limit cycles for a cubic Kolmogorov prey-predator system
    Lu, Zheng-yi
    He, Bi
    Gongcheng Shuxue Xuebao/Chinese Journal of Engineering Mathematics, 2001, 18 (04): : 115 - 117
  • [16] Nondegenerate centers and limit cycles of cubic Kolmogorov systems
    Algaba, Antonio
    Garcia, Cristobal
    Gine, Jaume
    NONLINEAR DYNAMICS, 2018, 91 (01) : 487 - 496
  • [17] Limit Cycles in a Cubic Kolmogorov System with Harvest and Two Positive Equilibrium Points
    Zhang, Qi-Ming
    Li, Feng
    Zhao, Yulin
    ABSTRACT AND APPLIED ANALYSIS, 2014,
  • [18] BIFURCATIONS OF LIMIT CYCLES FOR A PERTURBED CUBIC SYSTEM WITH DOUBLE FIGURE EIGHT LOOP
    Zhang, Tonghua
    Zang, Hong
    Tade, Mose O.
    INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2013, 23 (04):
  • [19] The limit cycles of a general Kolmogorov system
    Yuan, Yueding
    Chen, Haibo
    Du, Chaoxiong
    Yuan, Yuejin
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2012, 392 (02) : 225 - 237
  • [20] Limit Cycles Bifurcations for a Class of Kolmogorov Model in Symmetrical Vector Field
    Du Chaoxiong
    Liu Yirong
    Huang Wentao
    INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2014, 24 (03):
12345