具有年龄结构的三种群捕食与被捕食系统的最优生育率控制

Optimal Birth Control for Predator-prey Population Dynamics of Three Species with Age-structure

提出一类具有年龄结构的三种群捕食与被捕食系统,研究该系统的最优生育率控制问题。通过构造极值序列和Mazur定理证明了最优控制的存在性,利用法锥与共轭系统推导出模型的最优生育率控制的必要条件,为三种群的生育率控制问题提供了理论依据。

A three-species model of predator-prey population dynamics with age-structure is proposed,and the optimal birth control problem of this model is mainly studied.Firstly,the extremal sequence is constructed,and Mazur’s theorem is used to verify the existence of the optimal control problem.Next,the necessary conditions for the optimal birth problem of this model is derived out via normal cone and adjoint system,which can provide theoretical basis for fertility control of three populations.