捕食者带有疾病的入侵反应扩散捕食系统的空间斑图  

Spatiotemporal Pattern Formation of an Invasion-diffusion Predator-prey System with Disease in the Predator

作　　者：李成林[1] 

机构地区：[1]云南省红河州蒙自市红河学院数学学院

出　　处：《应用数学学报》2016年第6期832-846,共15页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(11461023);红河学院博士基金(14bs19)资助项目

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.This paper is purported to investigate an invasion-diffusion predator-prey epi- demic system in a bounded domain with no flux boundary condition. The local and global stabilities of positive equilibrium are investigated to this system without invasion-diffusion. The sufficient conditions to nonexistence and existence of non-constant positive solution are found for this invasion-diffusion epidemic system, and the existence of non-constant positive solution implies the existence of spatiotemporal pattern formation. The results show that in wide space for the predator and the prey to diffuse by the self pressure and with a little tendency of predator to catch prey, they can＇t coexist and there isn＇t endemic disease extensively, but they can coexist and endemic disease exists extensively when the coefficient of invasion-diffusion for predator is big enough with other random diffusion coefficients being fixed and satisfying curtain conditions.

关 键 词：定态解 稳定性 共存态 

分 类 号：O175.1[理学—数学]