具有阶段结构和同类相食的时滞捕食模型

Delayed Predator-Prey Model with Stage-Structure and Cannibalism

研究了一类食饵种群具有阶段结构、捕食者种群具有同类相食的时滞捕食模型.以捕食者种群的妊娠时滞为分岔参数,利用特征值法讨论了模型局部渐近稳定性和局部Hopf分岔存在性,推导出模型产生局部Hopf分岔的时滞临界点,并借助中心流形法分析了Hopf分岔的性质.

A delayed predator-prey model with stage-structure in prey population and cannibalism in predator population is studied in the present paper.Taking the pregnancy delay of predator population as the bifurcation parameter,local asymptotic stability and existence of local Hopf bifurcation of the model are discussed by using the eigenvalue method,and the critical value of the delay at which the local Hopf bifurcation exhibits is derived.Then,the properties of the Hopf bifurcation are studied by means of the central manifold method.Finally,a simulation example is performed to verify the correctness of the obtained results.