一类带负交叉扩散项二维系统的空间Turing斑图

吉林大学学报(理学版)

一类带负交叉扩散项二维系统的空间Turing斑图

张道祥^1,2, 赵李鲜^1, 孙光讯^1, 周文¹, 于艳¹

1. 安徽师范大学数学计算机科学学院, 安徽芜湖 241003； 2. 赫尔辛基大学数学与统计学院, 芬兰赫尔辛基 00014

收稿日期:2016-10-31 出版日期:2017-05-26 发布日期:2017-05-31
通讯作者: 张道祥 E-mail:18955302433@163.com

Spatial Turing Pattern of a Class of Two DimensionalSystem with Negative CrossDiffusion

ZHANG Daoxiang^1,2, ZHAO Lixian^1, SUN Guangxun^1, ZHOU Wen^1, YU Yan¹

1. School of Mathematics and Computer Science, Anhui Normal University, Wuhu 241003, Anhui Province,China； 2. Department of Mathematics and Statistics, University of Helsinki, Helsinki 00014, Finland

Received:2016-10-31 Online:2017-05-26 Published:2017-05-31
Contact: ZHANG Daoxiang E-mail:18955302433@163.com

摘要/Abstract

摘要： 考虑一类带负交叉扩散项二维系统的Turing斑图生成及其选择问题. 先利用稳定性理论和Hopf分支理论得到Turing斑图的存在区域, 再利用多重尺度分析法推导系统的振幅方程, 并给出Turing斑图的选择结果. 最后考虑一个具有比率依赖的HollingTanner捕食模型生态系统, 利用MATLAB软件对该模型的斑图生成及选择结果进行数值模拟, 得到了包括点状、条状以及二者共存等不同类型的Turing斑图.

关键词: 二维系统, Turing斑图, 振幅方程, 负交叉扩散系数

Abstract: We considered the generation and selection of Turing pattern of a class of two dimensional system with negative crossdiffusion. Firstly, the existence region of Turing pattern was obtained by using stability theory and Hopf bifurcation theory. Secondly, the amplitude equations of the system were derived by using multiscales analysis method, and the selection result of Turing pattern was given. Finally, we considered a specific ecosystem with a ratio dependent HollingTanner predatorprey model. MATLAB software was used to simulate the pattern generation and selection results of the model, and the different types of Turing patterns, such as dot, strip and the coexistence of the two types were obtained.

Key words: amplitude equation, two dimensional system, negative crossdiffusion coefficient, Turing pattern

中图分类号:

O175.21

张道祥, 赵李鲜, 孙光讯, 周文, 于艳. 一类带负交叉扩散项二维系统的空间Turing斑图[J]. 吉林大学学报(理学版), 2017, 55(03): 537-546.

ZHANG Daoxiang, ZHAO Lixian, SUN Guangxun, ZHOU Wen, YU Yan. Spatial Turing Pattern of a Class of Two DimensionalSystem with Negative CrossDiffusion[J]. Journal of Jilin University Science Edition, 2017, 55(03): 537-546.