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.
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页数：6
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