标题:
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A Delayed Predator-Prey Model with
Migration Rate and Holling-II Type Functional Response
作者:
段全恒, 郭志明
关键字:
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
期刊名称:
《Advances in Applied Mathematics》, Vol.3 No.4, 2014-11-28
摘要:
本文研究了一类捕食者具有人工控制迁移率的Holling-II型功能性反应的捕食-食饵模型的全局动力学性质。由于捕食者的捕食行为对其数量的变化有滞后效应，所以该模型是一个时滞微分方程组。首先研究了该系统平衡点的存在性和稳定性；接着以时滞为参数，分析Hopf分支存在的充分条件；利用中心流形定理和正规型理论给出确定Hopf分支周期解方向和稳定性的计算公式；最后对于理论结果给出了相应的数值模拟。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.