具有避难所的Lotka-Volterra竞争系统捕获分析  

Harvesting Analysis of a Lotka-Volterra Competitive System Incorporating a Refuge

作　　者：陈婉琳[1] 陈凤德[1] 王海娜[1] 林玉花[1] 

机构地区：[1]福州大学数学与计算机科学学院,福州350108

出　　处：《应用数学学报》2014年第6期1117-1129,共13页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(11201075);福建省自然科学基金(2011J01007);福建省科技创新平台计划项目(2009J1007)资助项目

摘　　要：研究了某一种群具有避难所的Lotka-Volterra竞争系统的捕获模型,通过计算雅克比矩阵的特征值以及构造适当的Ly印unov函数给出了保证系统正平衡点的局部稳定性和全局稳定性的充分性条件,我们的结果表明足够大的避难所可以确保两种群共存.文中考虑对两种群分别进行捕获,对于具有避难所的种群,捕获只能在避难所外进行.之后,我们分析了捕获对种群平衡密度的影响,发现在适当的限制下,捕捞努力量的变化对其中一个种群的平衡密度不产生影响.其后,获得了生物经济平衡点的存在性,并考虑了可对避难所内的种群进行捕捞的系统和不能对避难所内的种群进行捕捞的系统,分析和比较了两种情况下避难所对生物经济平衡点所产生的不同影响.最后,利用Pontryagin最大值原理得到了达到最优捕获的最优平衡解.A Lotka-Volterra competitive system incorporating a constant proportion of refuge for one species and independent harvesting in either species is studied in this paper. By caculating characteristic value of Jacobian matrix and constructing a suitable Lyapunov function, we show that the unique positive equilibrium of the system is locally stable and globally stable, which means enough large refuge could make two species coexist. After that, considering harvesting outside the refuge for one species incorporating a refuge, detailed analysis about the influence of harvesting is carried out, we find harvesting has no influence on the final density of one species under some suitable restricion. Then, the presence of bionomic equilibrium are obtained. And for one species incorporating a refuge, the different influence of refuge is obtained by comparing and analysing system of harvesting outside the refuge or inside the refuge. At last, the optimal harvesting policy is obtained by using the Pontryagin＇s maximal principle.

关 键 词：LOTKA-VOLTERRA竞争系统 避难所 全局渐近稳定 最优捕获 

分 类 号：O175.14[理学—数学]