具有非线性收获效应的捕食者-食饵系统的空间Turing斑图

doi:10.3969/j.issn.1000-5641.2018.04.002

华东师范大学学报(自然科学版) ›› 2018, Vol. 2018 ›› Issue (4): 9-22,31.doi: 10.3969/j.issn.1000-5641.2018.04.002

具有非线性收获效应的捕食者-食饵系统的空间Turing斑图

张道祥¹, 孙光讯¹, 胡伟¹, 凯歌²

1. 安徽师范大学数学与统计学院, 安徽芜湖 241002;
2. 北京工业大学机械工程与应用电子技术学院, 北京 100124

收稿日期:2017-09-20 出版日期:2018-07-25 发布日期:2018-07-19
作者简介:张道祥,男,博士,副教授,主要研究方向为微分方程理论及其应用.E-mail:zdxiang@ahnu.edu.cn
基金资助:
国家自然科学基金青年项目（11302002）；安徽师范大学2017年研究生科研创新与实践项目（2017cxsj040）

Spatial Turing pattern of a predator-prey system with nonlinear harvesting effect

ZHANG Dao-xiang¹, SUN Guang-xun¹, HU Wei¹, KAI Ge²

1. School of Mathematics and Statistics, Anhui Normal University, Wuhu Anhui 241002, China;
2. College of Mechanical Engineering and Applied Electronics Technology, Beijing University of Technology, Beijing 100124, China

Received:2017-09-20 Online:2018-07-25 Published:2018-07-19

摘要/Abstract

摘要： 研究了一类带有非线性食饵收获效应的捕食者-食饵系统的Turing斑图的生成及选择问题.首先利用稳定性理论给出了由交叉扩散项引起的Turing不稳定条件和分支理论分析得到了系统Turing斑图的存在区域，然后运用多重尺度分析法推导了系统的振幅方程，给出了Turing斑图的选择结果.最后利用Matlab软件对系统Turing斑图的生成和选择结果进行了数值模拟.结果展示了系统有丰富的Turing斑图，如点状、条状以及二者共存.

关键词: 捕食者-食饵系统, Hopf分支, Turing斑图, 振幅方程

Abstract: We study the formation and selection of Turing patterns for a class of predator-prey systems with nonlinear harvesting effect. Firstly, the conditions of Turing instability induced by cross-diffusion terms are given by stability theory, and the existence region of Turing patterns of the system are obtained by bifurcation theory. Secondly, the amplitude equations of the system are derived using the multi-scales analysis method, and the selection results of Turing patterns are given. Finally, Matlab is used to simulate the pattern formation and selection results of the system. The results show that the system has rich Turing patterns, such as spot, stripe, and coexistence of the two types.

Key words: predator-prey system, Hopf bifurcation, Turing patterns, amplitude equation

中图分类号:

O175.21

张道祥, 孙光讯, 胡伟, 凯歌. 具有非线性收获效应的捕食者-食饵系统的空间Turing斑图[J]. 华东师范大学学报(自然科学版), 2018, 2018(4): 9-22,31.

ZHANG Dao-xiang, SUN Guang-xun, HU Wei, KAI Ge. Spatial Turing pattern of a predator-prey system with nonlinear harvesting effect[J]. Journal of East China Normal University(Natural Sc, 2018, 2018(4): 9-22,31.

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具有非线性收获效应的捕食者-食饵系统的空间Turing斑图

Spatial Turing pattern of a predator-prey system with nonlinear harvesting effect

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