具有恐惧的捕食与被捕食系统的动力学分析  

Analysis of the Dynamic Model in a Predator-Prey System with the Impact of Fear

作　　者：夏增琼 李桂花[1] 

机构地区：[1]中北大学理学院,山西太原030051

出　　处：《数学的实践与认识》2017年第20期277-282,共6页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11201434);山西省留学回国人员科技活动择优资助项目

摘　　要：建立一类考虑捕食者受到恐惧的捕食与被捕食模型,用于研究连续变化的恐惧对某一地区食物链的影响,其中恐惧主要影响捕食者的捕食率,并分析了模型的动力学性态,利用第二加性复合矩阵证明了正平衡点的全局稳定性.分析发现在失去大型食肉动物的食物链中,对中型捕食者加入恐惧,可以避免中型捕食者数量突然爆发,同时有利于食物链下方生物的多样性.In this paper, a predator-prey model with predators suffered fear is explored in order to study how continuous variation fear affect the food chain in a certain region, which fear affect the predation rate of predator, whilst the dynamic behaviors of the model is investigated. In this paper, using the Second additive compound matrix we prove the global stability of the equilibrium. Results show that if large carnivore became extinct in food chain, threating mesocarnivore not only contributes to avoid outbreak of mesocarnivore population but it also protects species diversity in the lower trophic levels.

关 键 词：恐惧 捕食与被捕食 第二加性复合矩阵 平衡点 稳定性 

分 类 号：O175[理学—数学]