一类四次Kolmogorov系统的极限环分支  

Bifurcation of Limit Cycles for a Class of Quartic Kolmogorov System

作　　者：吴岱芩 黄文韬[1,2] 吴燕兰[1] 

机构地区：[1]桂林电子科技大学数学与计算科学学院,广西桂林541004 [2]贺州学院数学系,广西贺州542800

出　　处：《河南科技大学学报（自然科学版）》2016年第3期82-86,9,共5页Journal of Henan University of Science And Technology:Natural Science

基　　金：国家自然科学基金项目(11261013);广西高校重点实验室基金项目

摘　　要：研究了一类四次Kolmogorov系统在正平衡点(1,1)处的极限环分支问题。运用计算机代数系统Mathematica计算其伴随复系统的前5个奇点量,并给出正平衡点(1,1)成为五阶细焦点的条件,再利用雅克比行列式方法证明正平衡点(1,1)处可分支5个小振幅极限环。The bifurcation of limit cycles for a class of quartic Kolmogorov's system was investigated at the positive equilibrium point( 1,1). The first five singular point values of accompanied complex system were calculated by using computer algebra system Mathematica,and the conditions of the positive equilibrium point( 1,1) to be the five degree fine focus were deduced. Finally,five small amplitude limit cycles bifurcating from the positive equilibrium( 1,1) point were proved by Jacobi determinant method.

关 键 词：KOLMOGOROV系统 正平衡点 极限环 奇点量 

分 类 号：O175.12[理学—数学]