时滞种群生态系统的分支与最优策略研究

In the ecological resources,population resources is an important renewable resources,but it is not inexhaustible.Only scientific management and utilization can protect the ecological balance of nature.Therefore,the study of population dynamics system,especially the system optimal strategy,is of great significance and application value in ecology and economics.The purpose of this project is to study the factors of tax revenue on the basis of the study of time delay and diffusion population system..Firstly,the dynamic behavior of the population system is studied by means of the stability theory and bifurcation theory of dynamical systems.Secondly,the optimal equilibrium solution is obtained by using the Pontryagin maximum principle or the Fister analysis method.Finally, in order to support and test the reliability and practicability of our theoretical system,this project is to establish a model of natural enemies and pesticides taking Ningxia grassland rodent as the research object.And it obtained the optimal amount of Natural enemies and the optimal quantity of On the rodent pesticide through the analysis of the modelin in order to prevent the damage of rats to provide a theoretical basis.Moreover,we give the corresponding numerical simulation..Through four years of construction,this paper intends to establish a set of optimal control strategy system for the population dynamic system, which provides the necessary supply and guarantee for the local economic development and human survival and development.

在生态系统中,种群资源是一种重要的可再生资源,但并非取之不尽,用之不竭的.只有科学的管理和利用,才能保障大自然的生态平衡.因此种群动力系统的研究特别是系统最优策略的研究在生态学和经济学等方面都有重大意义和应用价值.本项目旨在时滞和扩散种群系统的研究基础上来考虑税收因素问题.首先,借助于动力系统稳定性理论和分支理论等来研究种群系统的动力行为,其次,运用Pontryagin最大值原理或利用Fister的分析方法对最优策略进行分析得到最优平衡解.最后,为支持与检验我们的理论体系的可靠性与实用性,以宁夏草原鼠害为研究对象,建立投放天敌和杀虫剂模型,通过分析模型得出投放天敌的最优数量和灭鼠投放杀虫剂的最优量,为防止鼠害发生提供理论依据,并给出相应的数值模拟.通过四年的建设,拟建立起一套种群动力系统的最优控制策略体系,为地方经济发展和人类的生存与发展提供必要的供给与保障.

在生态系统中,种群资源是一种重要的可再生资源,但并非取之不尽,用之不竭的.只有科学的管理和利用,才能保障大自然的生态平衡.因此种群动力系统的研究特别是系统最优策略的研究在生态学和经济学等方面都有重大意义和应用价值.本项目旨在时滞和扩散种群系统的研究基础上来考虑税收因素问题.首先,借助于动力系统稳定性理论和分支理论等来研究种群系统的动力行为,其次,运用Pontryagin最大值原理或利用Fister的分析方法对最优策略进行分析得到最优平衡解.最后,为支持与检验我们的理论体系的可靠性与实用性,以宁夏草原鼠害为研究对象,建立投放天敌和杀虫剂模型,通过分析模型得出投放天敌的最优数量和灭鼠投放杀虫剂的最优量,为防止鼠害发生提供理论依据,并给出相应的数值模拟.通过四年的建设,拟建立起一套种群动力系统的最优控制策略体系,为地方经济发展和人类的生存与发展提供必要的供给与保障.