AAM  >> Vol. 3 No. 4 (November 2014)

    A Delayed Predator-Prey Model with Migration Rate and Holling-II Type Functional Response

  • 全文下载: PDF(823KB) HTML    PP.231-244   DOI: 10.12677/AAM.2014.34033  
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时滞微分方程系统Holling-II型功能性反应迁移率稳定性Hopf分支Delayed Differential System Holling-II Functional Response Migration Rate Stability Hopf Bifurcation



In this paper, we study global dynamic properties of a predator-prey model with Holling-II func- tional response and predator migration, which reflect manual control. Because of the delay effect of predations on the variation of predator’s quantity, this model is a system of delayed differential equations. Firstly, we study the existence and stability of equilibria. Then, sufficient conditions are obtained which ensures that Hopf bifurcation occurs when the delay is regarded as a bifurcation parameter. We also derive computational formula for direction and stability of Hopf bifurcation by applying the center manifold theorem and norm form theory. Some numerical simulations illu-strate the theoretical results.

段全恒, 郭志明. 一类具有迁移率和Holling-II型功能性反应的时滞捕食–食饵模型[J]. 应用数学进展, 2014, 3(4): 231-244. http://dx.doi.org/10.12677/AAM.2014.34033


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