具有经济临界值的非光滑捕食与被捕食系统的全局稳定性分析(英文)  

Global Analysis for Non-Smooth Prey-Predator Model with Economic Threshold

作　　者：孔小丽[1] 唐三一[1] 

机构地区：[1]陕西师范大学数学与信息科学学院,陕西西安710062

出　　处：《生物数学学报》2012年第3期413-423,共11页Journal of Biomathematics

基　　金：Supported by the National Natural Science Foundation of China(11171199);by the Fundamental Research Funds for the Central Universities (GK201003001)

摘　　要：只要害虫种群数量在经济临界值水平之上就连续的实施综合控制策略,基于此本文提出了具有经济临界值的非光滑捕食与被捕食系统.我们给出了系统真平衡态、假平衡态和伪平衡态的存在性和稳定性,以及这些平衡态全局稳定或系统存在全局吸引子的条件,同时借助数值方法验证了所得结论.得到的主要结果说明通过采用临界控制策略能让害虫稳定在一个给定的临界值水平上,而达到害虫控制的目的.In present work we have developed a non-smooth prey-predator model with economic threshold,and assume that we only implement the integrated control measures once the density of pest population is larger than the economic threshold. The existence and stability of regular,virtual and pseudo-equilibria are investigated, and some sufficient conditions which guarantee the global stability or global attractor of those equilibria are provided.Further,numerical investigations on non-smooth predator-prey model are carried out to confirm our main results.The results obtained here indicate that we can maintain the density of pest population stabilize at a given threshold level through threshold policy control.

关 键 词：非光滑动力系统 捕食-被捕食系统 经济临界值 Lambert W函数 滑动模态 李雅普诺夫函数 

分 类 号：Q145[生物学—生态学]