无穷时滞单种群Logistic捕获模型的渐近行为  

Asymptotical behavior of a infinite delay single Logistic species harvesting system

作　　者：吴怀弟[1] 张娜[1] 陈凤德[1] 

机构地区：[1]福州大学数学与计算机科学学院,福建福州350108

出　　处：《福州大学学报（自然科学版）》2011年第3期325-328,共4页Journal of Fuzhou University(Natural Science Edition)

基　　金：福建省科技创新平台计划资助项目(2009J1007)

摘　　要：研究一类具捕获的无穷时滞单种群Logistic模型.首先证明过渡捕捞将使得种群最终走向绝灭,其后对一般情形的积分核,通过构造适当的Lyapunov泛函,得到保证系统正平衡点全局吸引的充分性条件.在具有弱时滞积分核时,通过变换和构造适当的Lyapunov一函数,证得系统的稳定性只跟人类捕获有关.而跟时滞无关.以上述结论为基础最后进一步探讨了种群的最优捕获问题.In this paper, a single species population dynamics with infinite delay and harvesting is proposed. We first show that excess harvesting will lead to the extinction of the species. Next, by constructing a suitable Lyapunov function, sufficient condtions are obtained to guarantee the global attracitivity of the positive able variable change equilibrium of the system. For the weakly and constructing a suitable Lyapunov tive equilibrium is globally attractive if it exist, and delay kernal case, by giving a suit-function, we are able to show that the posihas no intlunence on the stability property of the system. Finally, the effect of harvesting to economic profit is studied, and the capture effort of the species is investigated in order to obtain the maximum economic profit.

关 键 词：无穷时滞 LOGISTIC模型 LYAPUNOV泛函 稳定性 

分 类 号：O175.14[理学—数学]