一类三次Kolmogorov系统的极限环  

Limit cycles of a cubic 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：《桂林电子科技大学学报》2016年第2期160-163,共4页Journal of Guilin University of Electronic Technology

基　　金：国家自然科学基金(11261013)

摘　　要：针对一类三次Kolmogorov捕食系统在正平衡点(1,1)的极限环分支问题,利用计算机代数系统Mathematica,将实系统逐步转化为复系统,计算伴随复系统的前5个奇点量,利用雅克比行列式推导正平衡点处可分支的极限环个数,得出该系统在一定条件下可分支5个小振幅极限环的结果。Aiming at bifurcations of limit cycles of a cubic Kolmogorov predator-prey system at the positive equilibrium point （ 1,1 ）, the real system is translated gradually into a complex system by the computer algebra system Mathematica, then the first five singular point values for the concomitant complex system are calculated, and the numbers of limit cycles at the positive equilibrium point can be deduced by Jacobi determinant. Five small amplitude limit cycles bifurcating from the positive equilibrium point can be concluded in the certain conditions.

关 键 词：正平衡点 KOLMOGOROV系统 极限环 奇点量 

分 类 号：O175.12[理学—数学]