关于常数和比例投放天敌的最优控制策略

The optimal control strategy with constant and proportion releasing natural enemy

利用所建立的害虫-天敌系统模型,在假设单位农药成本和投放单位天敌成本已知的条件下研究如何控制杀虫剂的剂量和投放天敌的数量,使得经济效益达到最大的问题.利用极大值原理,LambertW函数的定义和性质以及Lagrange乘子条件得到了只采用一次化学控制,一次生物控制和一次综合化学和生物控制下的最优经济利益的存在性,并比较3种不同策略下最大的最优经济效益.结果显示综合控制的成本是最优的.

The main purposes of thesis focus on how the dosage of pesticide applications is controlled and the number of releasing of natural enemies can be maximized when knowing the cost of pesticide application and the cost of releasing natural enemies with model of Pest-natural enemy system.Through the maximum principle,Lambert W function and Lagrange multiplier condition,in particular,for one time impulsive effect three different control strategies（one time chemical control,one time biological control and the combination both） in terms of cost are compared.The results indicate that the integrated control strategy is the optimal.