摘要
利用常微分方程的定性理论,讨论了2个种群具有非线性密度制约的捕食-被捕食者系统:ddxx=b0x(b1+b2x-b3x2)-b4xy,ddyt=-cy+(ax-βy)y的平衡点和极限环的问题,证明了当系统的参数有如下关系时a2=(2k-1)+1-2xa14-2k,系统存在Hopf分支.同时证明了由Hopf分支所产生的周期解的稳定性.
By using the qualitative theory of the ordinary differential equation,we investigate a predator prey model of two populations：dx/dx=b0x（b1＋b2x-bsx^2）-b4xy,dy/dt=-cy＋（ax-βy）y The equilibrium points and limit cycles in the model are discussed. It is shown that the model undergoes a Hopf bifurcation when the parameters have the relationship：a2=（2k-1）＋1-2a1-2k/x4,and proved that the periodic solution created by the Hopf bifurcation is stable.
出处
《甘肃科学学报》
2006年第1期22-26,共5页
Journal of Gansu Sciences
基金
扬州职业大学重点科研项目(04K03)
关键词
平衡点
极限环
HOPF分支
equilibrium points
limit cycles
Hopf bifurcation
