入侵反应扩散捕食系统的时空斑图（英文）  

Spatiotemporal Pattern Formation of an Invasion-Diffusion Predator-Prey System

作　　者：李成林[1] 

机构地区：[1]红河学院,蒙自661199

出　　处：《系统科学与数学》2017年第3期950-964,共15页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(11461023);红河学院硕博基金(14bs19)资助课题

摘　　要：研究了一类具有HollingⅡ型反应函数和Neumann边界条件的入侵反应扩散捕食模型.考察了局部稳定性和全局稳定性,找到了非常数正解存在和不存在的充分条件,这些条件说明了时空斑图存在的可能性.研究结果表明在空间很大的地域上,捕食者和食饵在自扩散压力下自由扩散,但捕食趋向很小的情况下,二者不能生存.当入侵反应扩散系数足够大且其它扩散系数有上界时,两物种就能共存,从而形成一定的时空斑图.This paper is purported to investigate an invasion-diffusion system arising in a predator-prey population model with Holling type-II functional response in a bounded domain with no flux boundary condition. The local and global stabilities are investigated to this system. We find the sufficient condition to nonexistence and existence of non-constant positive solutions for this invasion-diffusion model, which implies the possible 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 not coexist, but they can coexist when the coefficient of invasion-diffusion for predator is big enough with other diffusion coefficients being bounded above.

关 键 词：定态解 稳定性 共存态. 

分 类 号：O175[理学—数学]