CAJ | 학술논문

研究了由Gilpin-Ayala模型描述的种群系统的优化控制问题。首先研究在周期环境下的Gilpin-Ayala种群系统的收获问题，研究了系统周期解的存在性及稳定性，并利用关于微分系统的极值原理和一些分析技巧，获得了最优控制策略及最优收益的确切表达式。其次研究了一类非自治Gilpin-Ayala收获系统在给定时间范围内的最大收益问题，对于不同的初值条件，获得了最优收获策略，以保证在给定的时间范围内能够获得最大的收获量。
연구료유Gilpin-Ayala모형묘술적충군계통적우화공제문제。수선연구재주기배경하적Gilpin-Ayala충군계통적수획문제，연구료계통주기해적존재성급은정성，병이용관우미분계통적겁치원리화일사분석기교，획득료최우공제책략급최우수익적학절표체식。기차연구료일류비자치Gilpin-Ayala수획계통재급정시간범위내적최대수익문제，대우불동적초치조건，획득료최우수획책략，이보증재급정적시간범위내능구획득최대적수획량。
In this paper ,we investigate the optimal control problems of nonautonomous Gil-pin-Ayala harvesting models .For a periodic Gilpin-Ayala control system ,the existence and stability of positive periodic solution is discussed and by choosing the harvest effort as con-trol variable ,the exact expressions of the optimal control strategy and the optimal profit are obtained by maximum principle of differential system and some analysis techniques .Also ,by choosing the harvesting rate as control variable ,we study a maximum harvesting problem in given time range for a general nonautonomous Gilpin-Ayala system ,the optimal harvesting policy is determined respectively for the different initial conditions .