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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2016, Vol. 33 ›› Issue (6): 651-660.doi: 10.3969/j.issn.1005-3085.2016.06.007

• • 上一篇    

一类带有非线性边界条件的捕食-食饵模型的正解的稳定性(英)

高 瑜, 李艳玲   

  1. 陕西师范大学数学与信息科学学院，西安 710062
  • 收稿日期:2015-06-16 接受日期:2015-11-25 出版日期:2016-12-15 发布日期:2017-02-15
  • 基金资助:
    中央高校基本科研业务费专项资金 (GK201401004).

Stability of Steady States for the Holling-Tanner Predator-prey Model with Nonlinear Boundary Conditions

GAO Yu, LI Yan-ling   

  1. College of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710062
  • Received:2015-06-16 Accepted:2015-11-25 Online:2016-12-15 Published:2017-02-15
  • Supported by:
    The Fundamental Research Funds for the Central Universities (GK201401004).

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摘要： 本文讨论了一类带有非线性边界条件的捕食-食饵模型，此模型比相应具有线性边界条件的模型具有更加广泛的应用价值．我们利用格林公式证明了一类特征值问题的所有特征值都是正的，利用局部分歧理论证明了模型正解的存在性，进一步，我们利用扰动理论建立了分歧解的渐近稳定性．为了支持和补充分析结果，我们最后利用Matlab软件进行了数值模拟．

关键词: 捕食-食饵, 非线性边界, 分歧, 稳定性

Abstract: In this paper, we consider a diffusion predator-prey model with nonlinear boundary conditions, which has more extensive application areas than the corresponding model with linear boundary conditions. We first show that all eigenvalues of a class of eigenvalue problems are positive by using Green's identity. The existence of positive solutions is also established by using the bifurcation theory. Moreover, we discuss the asymptotic stability of bifurcation solutions with the help of the perturbation theory. Finally, we give some examples of numerical simulations by Matlab to support the analytical results.

Key words: predator-prey, nonlinear boundary conditions, bifurcation, stability

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