具脉冲收获logistic系统的优化问题研究

Optimization Research on the Logistic System with Impulsive Harvesting

研究一类具脉冲收获的自治logistic模型的优化控制问题。首先考虑了如何投放鱼苗可以使得种群在(0,τ)内增量最大;其次在增量最大的前提下,每隔时间τ对种群同时进行比例和常量脉冲收获,以最大经济净收益为目标,讨论最优脉冲收获策略。

A kind of optimal control problem modeled by autonomous logistic equation with impulsive harvesting is studied. Firstly, the corresponding condition that makes the population obtain the maxi- mum increment is obtained. Secondly, under the precondition of maximum increment, the species is harvested with both the proportional and constant harvesting every time. Aiming at the maximum eco- nomic net revenue, the optimal impulsive harvesting policy is investigated.