具有脉冲扩散的近远海渔业系统的周期优化收获策略

OPTIMAL CONTROL POLICY OF A CLASS OF INSHORE-OFFSHORE FISHERY MODEL WITH IMPULSIVE DIFFUSION AND HARVESTING

研究了一类在周期环境中具有脉冲扩散及收获的近远海渔业系统的动力学行为和优化控制问题.系统中近远海鱼群每隔一定时间进行一次迁移扩散,为了经济利益对近海鱼群进行比例收获.在系统保持周期变化的条件下,选择收获努力量为控制变量,考虑收获成本因素,以一个周期内经济净收益最大为目标研究最优收获策略.首先研究了收获系统周期解的存在性和稳定性,并利用脉冲微分系统的极值原理获得了周期优化控制策略的具体表达式.

In this paper, we consider the dynamic behavior and optimal harvesting control of inshore-offshore fishery systems with periodic coefficients. We suppose that the inshore and offshore subspecies diffuse each other impulsively, and that the inshore species are harvested for economic profit. The purpose is to control the harvesting effort so as to maximize the profit which is the difference between economic revenue and cost. We investigate the existence and stability of periodic solutions, and obtainfurther the explicit expression of the optimal control policy by the maximum principle for optimal impulse control problem.