捕食者带有疾病的入侵反应扩散捕食系统的空间斑图

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捕食者带有疾病的入侵反应扩散捕食系统的空间斑图李成林云南省红河州蒙自市红河学院数学学院, 蒙自 661199 Spatiotemporal Pattern Formation of an Invasion-diffusion Predator-prey System with Disease in the Predator LI ChenglinDepartment of Applied Mathematics, Honghe University, Mengzi 661199, China

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摘要本文考察了一类在有界区域内在零流边界条件下捕食者带有疾病的入侵反应扩散捕食系统.在没有入侵反应扩散的条件下考虑了这类系统的局部和全局稳定性.找到了具有入侵反应扩散系统的非常数定态解存在性和不存在性的充分条件，其存在预示着空间斑图的形成.文中结论表明当物种的生存空间很大，捕食者的捕食趋向很小时，没有空间斑图出现，两物种不能共存且没有疾病广泛传播.当入侵反应扩散系数很大，自扩散系数固定时，空间斑图出现，两物种能共存，这时疾病也广泛存在.

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收稿日期: 2015-05-18

PACS:

O175.1

基金资助:中国人民大学科学研究基金（中央高校基本科研业务费专项资金资助）项目成果（No.15XNL008）.

引用本文:

李成林. 捕食者带有疾病的入侵反应扩散捕食系统的空间斑图[J]. 应用数学学报, 2016, 39(6): 832-846. LI Chenglin. Spatiotemporal Pattern Formation of an Invasion-diffusion Predator-prey System with Disease in the Predator. Acta Mathematicae Applicatae Sinica, 2016, 39(6): 832-846.

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