不育控制下食饵-捕食者模型的Hopf分支

不育控制是害鼠治理的一种方法.害鼠种群与其他种群有着各种各样的联系,当害鼠种群在不育控制下改变其动力学行为时,与其相关的种群也随着改变其行为.建立了食饵-捕食者模型,其中害鼠是捕食者,对其进行不育控制.利用Hurwitz判据、中心流型定理、形式级数法、Hopf分支理论等分析了模型平衡点的稳定性和Hopf分支现象.有时,随着不育率增加,害鼠数量线性减少,其食饵数量线性增加;有时,不育控制会使害鼠及其食饵数量大幅度周期变化.因此,进行不育控制前,要对害鼠及其食饵有充分的了解,选择适当的不育率.

Hopf bifurcation of one prey-predator model with contraception control

Contraception control is a new method to control rodent pest.Due to the complex relation between rodent population and other populations,when contraception control was implemented to rodent, the dynamical behavior of rodent population and other related populations would alter.A prey-predator model was formulated and analyzed to investigate the effect of contraception control on population dynamics of rodent and its prey.In the model,rodent was predator and was controlled with sterilant.The stability of equilibriums and Hopf bifurcation phenomenon were analyzed by means of Hurwitz criterion,Lasalle invariance principle,center manifold theorem,formal series method and Hopf bifurcation theory.Sometimes,along with the increasing of contraception rate,the amount of rodent will decrease linearly and the amount of prey would rise linearly.Sometimes, the contraception control may result in the amount of rodent and its prey varying periodically in a large extent and the result was awful.Therefore,before implementing the contraception control,understanding the relation of rodent and its prey fully and selecting a suitable contraception rate were necessary.