引用本文:康举, 黄头生, 孟天祥, 张化永.Holling-II型三种群食物网模型的Hopf分岔行为研究[J].西南大学学报(自然科学版),2019,41(5):64~71
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Holling-II型三种群食物网模型的Hopf分岔行为研究
康举, 黄头生, 孟天祥, 张化永
华北电力大学 工程生态学与非线性科学研究中心, 北京 102206
摘要:
构建了Holling-Ⅱ型三种群食物网模型,利用Jacobian矩阵、Routh-Hurwitz判据、Hopf分岔和中心流形等理论分别讨论了系统的局部渐进稳定性和Hopf分岔的发生条件.通过数值模拟,展示了食物网系统的Hopf分岔行为,揭示了种群动态随外界参数条件的变化以及随时间演化的分布规律.
关键词:  食物网模型|局部渐进稳定性|Hopf分岔|数值模拟
DOI:10.13718/j.cnki.xdzk.2019.05.011
分类号:O175.14;Q141
基金项目:国家“十三五”重大科技专项(2017ZX07101-002);中央高校基本科研业务费专项(JB2017069).
Study on Hopf Bifurcation in a Three-Species Food Web Model with Holling-Ⅱ Functional Response
KANG Ju, HUANG Tou-sheng, MENG Tian-xiang, ZHANG Hua-yong
Research Center for Engineering Ecology and Nonlinear Science, North China Electric Power University, Beijing 102206, China
Abstract:
We investigated a three-species food web model with Holling-Ⅱ functional response. Jacobian matrix, Routh-Hurwitz criteria, Hopf bifurcation theorem and central manifold theorem were used to analyze local asymptotic stability and to determine Hopf bifurcation condition for the food web system. The Hopf bifurcation of the system was demonstrated by numerical simulations. The dynamics behaviors revealed change of population dynamics with variations of the parameters as well as time evolution.
Key words:  food web model|local asymptotic stability|Hopf bifurcation|numerical simulations
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