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| 摘要: |
| 本文研究了带有负交叉扩散项的SIR传染病模型的空间斑图动力学问题.利用稳定性理论和Hopf分支理论，获得了Turing失稳的条件以及Turing斑图的存在区域，并且利用Matlab软件模拟获得了不同类型的Turing斑图，比如点状、条状以及二者共存等Turing斑图.通过负交叉扩散诱导出规则斑图，推广了负扩散效应对空间斑图的形成具有巨大影响的结果. |
| 关键词: SIR传染病模型 负交叉扩散系数 Turing斑图 |
| DOI： |
| 分类号:O175.21 |
| 基金项目: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）. |
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| SPATIAL TURING PATTERN IN SIR EPIDEMIC MODEL WITH NEGATIVE CROSS-DIFFUSION |
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ZHOU Wen,HU Wei,CHEN Jin-qiong,KAI Ge
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| Abstract: |
| In this paper, spatial pattern of SIR epidemic model with negative cross diffusion is considered. By performing a linear approach around the positive steady states of the model and Hopf bifurcation theorem, sufficient conditions are obtained for the Turing instability. And Turing region in which there are plenty of complicate spatial patterns is derived. Finally, some numerical simulations are given to certify that Turing patterns, such as spot, stripe and mixture of spot-stripe patterns. The regular pattern is induced by negative cross diffusion, which generalizes the results that negative cross diffusion has great influence on the spatial pattern formation. |
| Key words: SIR epidemic model negative cross-diffusion Turing pattern |
