一类三维生态动力系统的Hopf分支  

Hopf Bifurcation in the Third-Dimensional Ecologic Dynamical System

作　　者：吴云华[1] 袁晓凤[1] 刘世泽 

机构地区：[1]中国科学院成都计算所数理室,成都610041

出　　处：《数学物理学报（A辑）》1998年第1期70-77,共8页Acta Mathematica Scientia

摘　　要：考虑一类具偏食习惯的捕食者与被捕食者模型．利用中心流形定理和 Hopf分支理论讨论并证明了该系统在一定条件下产生Hopf分支，得到中心流形、小振幅空间周期解的渐近表达式，同时给出了周期解稳定性判据．A class of ecology models in predator-prey systems is considered. The bifurcationphenomena are discussed by using Hopf bifurcation and Center manifold theorems. Hopf bifurcation can occur in some values of parameters. The asymptotic formulas fot the center manifoldand the periodic solution with small amplitude have been given. The stable criterion of the periodic solution has also been obtained.

关 键 词：中心流形 HOPF分支 周期解 三维生态动力系统 

分 类 号：Q141[生物学—生态学]