一类功能性反应模型在常数收获下的动态特性

The Dynamical Characteristic of a Functional Response Model with Constant Harvest

具有功能性反应的捕食与被捕食模型具有非常复杂的动态性质．特别是在常数收 获下,该模型呈现了各种各样、纷杂多变的动态特性,其中包括正平衡点及其稳定性的变化、各 种分叉的产生以及周期解和极限环的出现．本文重点研究了常数收获项对一类功能性反应模型的 动态性能的影响,得到了该收获模型存在稳定正平衡点、产生分叉以及在Hopf分叉附近产生周 期解和极限环的若干充分条件．

The predator-prey model with a functional response has very complicated dynamic properties. Especially under some constant harvest, this model displays various complicated dynamic feature, including changes of the positive equilibrium and stability, as well as emergence of bifurcation, periodic solutions and limit cycles. In this paper, we mainly study the effect of constant harvest on the dynamical characteristic for such model, obtain some conditions for such model to have stable positive equilibrium, bifurcation, periodic solutions and limit cycles.