带有食饵保护的Holling-Ⅲ型扩散捕食系统的稳定性分析(英文)  

Stability Analysis of a Diffusive Holling-Ⅲ Type Predator-prey System Incorporating a Prey Refuge

作　　者：史红波[1] 

机构地区：[1]淮阴师范学院数学科学学院,江苏淮安223300

出　　处：《工程数学学报》2012年第3期462-468,共7页Chinese Journal of Engineering Mathematics

基　　金：The National Natural Science Foundation of China(10801065);the Natural Science Foundation for Universities of Jiangsu Province(11KJB110003)

摘　　要：本文研究了一类具食饵保护的Holling-Ⅲ型扩散捕食系统,带有齐次Neumann边界条件.首先,讨论了系统的全局吸引性;其次,给出了系统正常数平衡态局部/全局渐近稳定的充分条件,这些条件依赖于食饵保护参数;特别地,获得了扩散对系统常数平衡态稳定性的影响,即当扩散系数较大时可使得常数平衡态不稳定.This paper is concerned with a diffusive predator-prey system with Holling III type func- tional response incorporating a prey refuge under homogeneous Neumann boundary con- ditions. Firstly, the global attractivity of this system is discussed. Then, some sufficient conditions which are dependent on the prey refuge parameter for the local/global asymp- totic stability of the positive constant steady state are given. In particular, the effect of diffusion on the stability of positive constant steady state is observed, that is, the large diffusion can make the positive constant steady state to be unstable.

关 键 词：捕食系统 Holling-III型功能反应 食饵保护 扩散 稳定性 

分 类 号：O175.7[理学—数学]