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山东大学学报（理学版） ›› 2016, Vol. 51 ›› Issue (11): 115-122.doi: 10.6040/j.issn.1671-9352.0.2016.282

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具有Beddington-DeAngelis功能反应项的捕食-食饵扩散模型的稳定性

付娟,张睿,王彩军,张婧   

  1. 兰州交通大学数理学院, 甘肃 兰州 730070
  • 收稿日期:2016-06-17 出版日期:2016-11-20 发布日期:2016-11-22
  • 作者简介:付娟(1990— ), 女, 硕士研究生, 研究方向为生物数学. E-mail:1010545137@qq.com
  • 基金资助:
    国家自然科学基金资助项目(11561041,61563026)

The stability of a predator-prey diffusion model with Beddington-DeAngelis functional response

FU Juan, ZHANG Rui, WANG Cai-jun, ZHANG Jing   

  1. Department of Mathematics, Lanzhou Jiaotong University, Lanzhou 730070, Gansu, China
  • Received:2016-06-17 Online:2016-11-20 Published:2016-11-22

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摘要： 考虑了一类带有扩散的Beddington-DeAngelis捕食者-食饵模型。 通过线性化方法和构造Lyapunov函数得到弱耦合反应扩散系统非负平衡点的局部和全局渐近稳定性; 分析了交错扩散系统对非负平衡点稳定性的影响, 并且得到了交错扩散导致Turing不稳定的区域。

关键词: 自扩散, 交错扩散, 稳定性, Lyapunov函数, 捕食者-食饵模型

Abstract: We consider a diffusive predator-prey model with Beddington-DeAngelis functional response. First, the local and global asymptotic stabilities of the nonnegative equilibrium point of weakly coupled reaction-diffusion system are obtained by linearization and constructing Lyapunov function. Secondly, the effect of cross-diffusion coefficient on the stability of the nonnegative equilibrium point is discussed. The results show that cross-diffusion can induce Turing unstable region.

Key words: self-diffusion, stability, cross-diffusion, lyapunov function, predator-prey model

中图分类号: 

  • O175.29
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