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山东大学学报（理学版） ›› 2018, Vol. 53 ›› Issue (4): 85-94.doi: 10.6040/j.issn.1671-9352.0.2017.509

• • 上一篇    

带有Holling-III功能反应和线性收获效应的时滞扩散捕食者-食饵系统Hopf分支和空间斑图

张道祥,孙光讯,马媛,陈金琼,周文   

  1. 安徽师范大学数学计算机科学学院, 安徽 芜湖 241002
  • 收稿日期:2017-09-27 出版日期:2018-04-20 发布日期:2018-04-13
  • 作者简介:张道祥(1979— ), 男, 博士, 副教授, 研究方向为微分方程理论及其应用. E-mail:18955302433@163.com
  • 基金资助:
    国家自然科学基金资助项目(11302002,11671013)

Hopf bifurcation and spatial patterns in a delayed diffusive predator-prey system with Holling-III functional response and linear harvesting effect

ZHANG Dao-xiang, SUN Guang-xun, MA Yuan, CHEN Jin-qiong, ZHOU Wen   

  1. School of Mathematics and Computer Science, Anhui Normal University, Wuhu 241002, Anhui, China
  • Received:2017-09-27 Online:2018-04-20 Published:2018-04-13

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摘要： 研究了一类带有Holling-III功能反应和线性收获效应的时滞扩散捕食者-食饵系统的空间动力学。首先利用稳定性理论和分支理论得到了系统正平衡点局部稳定和Hopf分支的条件;然后利用规范型理论和中心流形定理得到Hopf分支的方向和分支周期解的稳定性;进一步地, Hopf分支的不稳定导致了系统空间斑图的形成;最后通过数值模拟验证了理论结果的正确性,展示了系统具有丰富的动力学行为。

关键词: 捕食者-食饵系统, Holling-III功能反应, Hopf分支, 时滞

Abstract: The spatial dynamics in a delayed diffusive predator-prey system with Holling-III functional response and linear harvesting effect is studied. Firstly, the local stability of positive equilibrium of the system and the condition of Hopf bifurcation are obtained by using the stability theory and the bifurcation theory. Secondly, the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions are determined by the normal form theory and the center manifold theorem.Furthermore, the instability of Hopf bifurcation leads to the formation of spatial pattern of system. Finally, the correctness of the theoretical results is verified by numerical simulations, which shows that the system has rich dynamic behavior.

Key words: predator-prey system, Hopf bifurcation, Holling-III functional response, delay

中图分类号: 

  • O175.21
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