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| 摘要: |
| 本文讨论了带有负交叉扩散项的SIR传染病模型的空间斑图的动力学问题. 利用稳定性理论和Hopf分支理论得到了Turing 失稳的条件以及Turing 斑图的存在区域. 并且利用Matlab 软件模拟得到了不同类型的Turing 斑图, 比如点状、条状以及二者共存等Turing 斑图. 结果显示负交叉扩散效应对空间斑图的形成具有很大的影响, 即负交叉扩散诱导出了规则斑图. |
| 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(No.11302002)和安徽师范大学研究生教育创新工程及质量提升(No.061709). |
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| Spatial Turing Pattern in SIR epidemic model with negative cross-diffusion |
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Zhou Wen
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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 obtained results show negative cross diffusion has great influence on the spatial pattern formation. In other words, the regular pattern is induced by negative cross diffusion. |
| Key words: SIR epidemic model negative cross-diffusion Turing pattern. |
