带自控能力的捕食模型正解存在性与数值模拟  

Existence and numerical simulation of positive solutions for predator model with self-limitation

作　　者：李莹[1] 王利娟[1] LI Ying;WANG Lijuan(Institute of Mathematics and Information Science, Baoji University of Arts and Sciences, Baoji, Shaanxi 721013, China)

机构地区：[1]宝鸡文理学院数学与信息科学学院,陕西宝鸡721013

出　　处：《计算机工程与应用》2016年第19期53-56,共4页Computer Engineering and Applications

基　　金：国家自然科学基金(No.11401356);宝鸡文理学院重点科研项目(No.ZK11138;No.ZK12043)

摘　　要：在齐次Dirichlet边界条件下,研究一类低密度食饵下,捕食者具有自控能力的捕食模型平衡态正解存在性。通过连续延拓意义下建立的连续算子,利用度理论给出了平衡态正解存在的充分条件,并对理论结果进行数值模拟。研究结果表明,只要捕食者和食饵的生长率适当大,则捕食者和食饵可以共存。The existence of steady-state positive solutions for a predator-prey model with low density prey and self-limitedpredator is studied under the homogeneous Dirichlet boundary conditions. Using the continuous operators established bycontinuous extension, a sufficient condition for the existence of steady-state positive solutions is given by the degree theory.Furthermore, the theoretical results are simulated by numerical method. The research shows that, the predator and preycan coexist as long as the growth rates of the predator and prey are large suitably.

关 键 词：捕食食饵模型 平衡态 数值模拟 

分 类 号：O175[理学—数学]