具有阶段结构的种群动力学系统的最优化策略

项目名称： 具有阶段结构的种群动力学系统的最优化策略

项目编号： No.61261044

项目类型： 地区科学基金项目

立项/批准年度： 2013

项目学科： 无线电电子学、电信技术

项目作者： 高建国

作者单位： 北方民族大学

项目金额： 48万元

中文摘要： 种群资源是一种重要的可再生资源,但并非取之不尽,用之不竭.如果对这些资源进行科学的管理和利用,这些资源就能够年复一年的持续繁殖再生,为人类的生存和发展提供必要的供给,同时维持生态平衡.因此种群资源在生物学和经济学方面都有重大意义.本项目主要研究具有时滞和阶段结构的种群生态系统,并在捕获模型中考虑税收因素.首先,通过分析相应特征方程根的情况,探究了平衡点稳定性,讨论Hopf分支的存在性.其次,在规范型和中心流型理论基础上,建立定量分析理论体系来判断Hopf分支产生的周期解稳定性和分支方向,同时,运用Pontryagin最大值原理对最优税收策略进行分析,得到最优平衡解和最优税收值.最后,为验证我们的结论,建立黄河鲶鱼最优捕获模型,给出相应的数值模拟.通过四年的建设,拟建立起一套具有阶段结构种群动力系统的最优控制策略体系,并且为地方经济发展提供相关的理论支持.

中文关键词： 时滞；阶段结构；持久生存；稳定性；最优策略

英文摘要： Population resources is a kind of important renewable resources,but it is not inexhaustible.If this kind of resource is managed and utilized scientifically,it will be bred to provide necessary food supply for human survival and development,and to keep the ecological balance.So it is significant to study in biology and economics. In this project,the population ecology systems with time-delay and stage structure are analysed.In the meantime,the tax factor is considered in prey model. Finally the stability and Hopf bifurcation of the equilibrium points are investigated by analyzing the distribution of the roots of associated characteristic equation. Then on the basis of the normal form theory and center manifold argument,the quantitative analysis of the theoretical system to determine the stability and the direction of periodic solutions of bifurcating from Hopf bifurcations are established.At the same time,the optimal tax policy by using Pontryagin's maximum principle is obtained,we also get the optimal equilibrium point and the optimal tax value through analyzing optimal tax policy.Finally,in order to verify our conclusions,we establish Yellow catfish optimal capture model.Some numerical simulations are also carried out for supporting the analytic results. Through four years study, we want to established the syst

英文关键词： Time delay；Stage structure；Permanence；Stability；Optimal policy