| 摘要: |
| 研究了一类具有交叉扩散的捕食食饵模型的斑图形成.证明了交叉扩散破坏了正平衡点的稳定性，得到了交叉扩散导致不稳的条件.另外，数值模拟结果不仅支持了该理论，还显示模型具有复杂的空间斑图：条状斑图、点状斑图以及点条混合斑图.研究结果表明交叉扩散在斑图的形成中起着重要的作用. |
| 关键词: 捕食食饵系统 交叉扩散 图灵不稳 斑图形成 |
| DOI：10.3969/J.ISSN.100-5137.2018.03.008 |
| 分类号:O175.26 |
| 基金项目:The National Natural Science Foundation of China (11571227) |
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| Turing instability and pattern induced by cross-diffusion in a predator-prey system |
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Wang Qiufang, Peng Yahong
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College of Science, Donghua University, Shanghai 201620, China
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| Abstract: |
| The phenomenon of pattern formation for predator-prey model with cross-diffusion is considered. We prove that cross-diffusion can destabilize the positive equilibrium which is stable for the self-diffusion reaction system. We also derive cross-diffusion-driven instability conditions. Moreover, our numerical simulations support our theoretical findings and exhibit that the model has complex spatial patterns:stripe pattern, spotted pattern and their coexistence. These results show that the cross-diffusion plays an important role in the pattern formation. |
| Key words: predator-prey system cross-diffusion Turing instability pattern formation |
