捕食者环境容纳量依赖于食饵的食饵-捕食者模型  

A Prey-Predator Model in Which the Carrying Capacity of Predator Depending on Prey

作　　者：刘汉武[1] 张凤琴[1] 李秋英[1] 

机构地区：[1]运城学院应用数学系,山西运城044000

出　　处：《应用数学》2017年第4期806-813,共8页Mathematica Applicata

基　　金：国家自然科学基金项目(11371313;61573016;61203228);山西省自然科学基金项目(2013011002-5)

摘　　要：本文建立捕食者环境容纳量依赖于食饵数量的食饵-捕食者模型,分析了模型解的全局性态.可能同时存在多个正平衡点,它们当中会有鞍点或鞍结点.除鞍点外每个正平衡点都有一个吸引域.高寒草甸植被与高原鼠兔之间的关系可以用所建立的模型来描述,利用模型参数的实际值分析了高寒草甸退化的原因和恢复策略.过度放牧、人类不合理活动的加剧、高原鼠兔天敌的减少都是高寒草甸退化的原因.相应地,通过合理放牧、规范人类活动、保护或招引高原鼠兔的天敌、药物控制可以恢复退化的高寒草甸.According to the fact that the carrying capacity of predator depends on the amount of prey, a prey-predator model is formulated and the global behavior of its solutions is analyzed. Multiple positive equilibriums may exist simultaneously and include saddle and saddle-node. Except saddle, ev- ery positive equilibrium has an attracting domain. In alpine meadow ecosystem, the relations between vegetation and plateau pika can be described by this model. Based on the virtual parameters, the cause of alpine meadow degrading and recovery strategy of degraded alpine meadow are investigated. Over grazing, increasing of unreasonable human activities, decreasing of natural enemy of plateau pilau are the causes resulting in alpine meadow degrading. Correspondingly, reasonable grazing, regulating human ac- tivity, protecting or attracting natural enemy of plateau pika, controlling plateau pika with rodenticide can recover the degraded alpine meadow.

关 键 词：食饵一捕食者模型 密度制约 全局性态 退化高寒草甸 

分 类 号：O175.13[理学—数学]