具有Ivlev功能反应的捕食-食饵模型在零解处的分歧  

Bifurcation from zero solution in a predator-prey system with Ivlev functional response

作　　者：吴建华[1] 杨文彬[1] 

机构地区：[1]陕西师范大学数学与信息科学学院,陕西西安710119

出　　处：《陕西师范大学学报（自然科学版）》2014年第6期1-7,共7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(GK201401004)

摘　　要：研究了一类齐次Dirichlet边界条件下具有Ivlev功能反应的捕食-食饵扩散模型.主要涉及的工具包括Lyapunov-Schmidt约化方法,隐函数定理和线性化方法.讨论了系统在零解处小分歧正解的存在性和渐近稳定性,并通过数值模拟分析补充了理论分析结果.The diffusive predator-prey system with Ivlev functional response is investigated under homogeneous Dirichlet boundary conditions.The main tools used here include the Lyapunov-Schmidt reduction method,implicit function theorem and linearized method.The existence of small positive solutions bifurcating from the zero solution of the system and the asymptotical sta-bility of the bifurcating positive solutions are discussed.Moreover,some numerical simulations are done to complement the analytical results.

关 键 词：捕食-食饵模型 Ivlev 功能反应 稳态分支 稳定性 

分 类 号：O175.1[理学—数学]