文章研究了一类三维Lotka-Volterra系统的Hopf分支问题。首先利用中心流形上奇点量的递推公式计算得出了正平衡点的前四个焦点量,然后证明了这类系统至少存在四个极限环的结论。
Hopf bifurcation is studied for a three dimensional Lotka-Volterra system. Firstly, a recursion formula for computation of the singular point quantities is given for the corresponding equation. Then four limit cycles are constructed, which gives an good example to the cyclicity of 3D Lotka-Volterra system.