摘要
主要研究了在有限的时间周期内,由Gompertz模型描述且具有脉冲收获的种群系统的优化控制问题.在脉冲收获量预先给定的前提下,以种群在周期末的存储量最大为目标,研究脉冲收获时刻的不同选择对存储量的影响并确定最优的收获策略.首先利用脉冲微分系统的极值原理,研究了获得最优收获时刻应满足的条件,并在时间周期充分长的情况下讨论了具有多次固定常量收获时的最优收获策略;进一步结合分析技巧研究了在给定时间范围内的最多收获次数及最优收获策略问题;最后给出一个实例及数值模拟以验证本文所得到的主要结论.
The optimal control of a population system modeled by Gompertz equation with im pulsive harvesting is studied within a finite time interval. The main aim of this study is to choose the optimal impulsive harvesting moment to obtain the maximum stock level of the population at the end of the time period, under the fixed intensity and number of times of impulsive harvesting. By the maximum principle of impulsive differential system, the condi- tion that the optimal harvesting moment should satisfy is discussed and the optimal harves- ting strategy is obtained for the case of long time period. Moreover, some analytical tech- niques are applied to study the most harvesting times and the optimal harvesting strategy within given time interval, and finally, some numerical simulations are also carried out.
出处
《陕西科技大学学报（自然科学版）》
2013年第3期161-166,共6页
Journal of Shaanxi University of Science & Technology
基金
国家自然科学基金项目(10971124
61070189)
关键词
Gompertz模型
脉冲收获
极值原理
最优脉冲时刻
Gompertz model
impulsive harvesting
the maximum principle of impulsive dif-ferential system
optimal harvesting moment
