摘要
研究了一类空间非齐次环境下的捕食-食饵扩散模型。在食饵弱增长情形下,利用分歧理论给出了两个半平凡解附近正解的存在性,并刻画了整体结构;在食饵强增长情形下,通过度理论和正则摄动理论给出了正解存在的充分条件:λ∈(0,min{λ1D(Ω0),1/m3}),μ∈(λm1/1-λm3,M]。鉴于空间环境的非齐次性和退化因素的存在,通过数值算例验证了相应理论结果。
A predator-prey diffusion model in heterogeneous environment is researched.For the case of weak growth of prey,the existence of positive solutions are obtained near two semi-trivial solutions by using the bifurcation theory;moreover,the global structure are given.Secondly,for the case of strong growth of prey,the sufficient conditions:λ∈(0,min{λ1D(Ω0),1/m3}),μ∈(λm1/1-λm3,M]for the existence of positive solutions are showed by the degree theory and the regular perturbation theory.Considering the spatial heterogeneity and the influence of the degradation factor,some simulations are done in order to verify the theoretical results.
出处
《陕西师范大学学报（自然科学版）》
CAS
CSCD
北大核心
2015年第1期13-18,共6页
Journal of Shaanxi Normal University：Natural Science Edition
基金
国家自然科学基金资助项目(11271236)
中央高校基本科研业务费专项资金项目(GK201302025
GK201303008
GK201401004)
关键词
扩散
空间非齐次
分歧理论
度理论
存在性
diffusion
spatial heterogeneity
bifurcation theory
degree theory
existence
