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

页数：6

共 6 条

[1]

COLEMAN CS, 1978, DIFF EQUAT, V1, P279

[2] SYSTEMS OF DIFFERENTIAL-EQUATIONS THAT ARE COMPETITIVE OR COOPERATIVE .5. CONVERGENCE IN 3-DIMENSIONAL SYSTEMS [J].