一类具成群防卫模型的定性分析

Qualitative Analysis of a Class of Model with Group Defence

考虑一类具有成群防卫模型dxdt=x(k - x2 ) ex - xy,dydt=-βy(ex -αx2 ) (x(0 )≥ 0 ,y(0 )≥ 0 ) ,讨论了该模型轨线的有界性 ,极限环的不存在性、存在性及 Hopf分支问题 .

A class of model with group defence dxdt=x(k-x 2)e x-xy, dydt=-βy(e x-αx 2) (x(0)≥0,y(0)≥0)is considered. Bounds of orbit of the model and the existence and non existence of limit cycle and Hopf bifurcation of the model (1) are discussed.