[1]张艳芳,陈文彦.一类带有扩散的捕食模型正解的存在性[J].东南大学学报(自然科学版),2010,40(3):660-662.[doi:10.3969/j.issn.1001-0505.2010.03.042]
 Zhang Yanfang,Chen Wenyan.Existence of positive solutions to a predator-prey model with diffusion[J].Journal of Southeast University (Natural Science Edition),2010,40(3):660-662.[doi:10.3969/j.issn.1001-0505.2010.03.042]
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一类带有扩散的捕食模型正解的存在性()
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《东南大学学报(自然科学版)》[ISSN:1001-0505/CN:32-1178/N]

卷:
40
期数:
2010年第3期
页码:
660-662
栏目:
数学、物理学、力学
出版日期:
2010-05-20

文章信息/Info

Title:
Existence of positive solutions to a predator-prey model with diffusion
作者:
张艳芳 陈文彦
东南大学数学系, 南京 210096
Author(s):
Zhang Yanfang Chen Wenyan
Department of Mathematics,Southeast University,Nanjing 210096,China
关键词:
Holling-Ⅳ型函数 不动点指数 存在性 捕食模型
Keywords:
Holling type-Ⅳ function fixed point index existence predator-prey model
分类号:
O175.25
DOI:
10.3969/j.issn.1001-0505.2010.03.042
摘要:
讨论了一类带有扩散和非单调响应函数——Holling Ⅳ型函数的捕食模型,其中边界条件为齐次Dirichlet边界条件.首先,将该问题等价为强耦合的椭圆型边值问题,利用最大值原理和上下解方法得到正解的先验估计.然后,将该椭圆型方程组转化为一个全连续算子,利用锥上的拓扑度理论,给出正解存在的充分条件.结果表明,当食物具有群体防御能力或者猎物出现厌食时,在一定的条件下,食物和猎物可以共存.
Abstract:
A predator-prey model with diffusion and a non-monotonic functional response,the Holling type-Ⅳ function, is discussed under homogeneous Dirichlet boundary conditions. First, the problem is equivalent to a strongly coupled elliptic boundary value problem and a priori estimate of positive solutions is deduced by means of the maximum principle and the upper and lower solution method. Then by changing the elliptic equations into a completely continuous operator and by combining with the topological degree theory in cones,sufficient conditions for the existence of positive solutions are given. Results show that the predator and prey can coexist when the prey has the ability of group defense or when anorexia response occurs on the predator population.

参考文献/References:

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备注/Memo

备注/Memo:
作者简介: 张艳芳(1985—),女,硕士生; 陈文彦(联系人),女,博士,副教授, cwyseu@163.com.
基金项目: 国家自然科学基金资助项目(10601011).
引文格式: 张艳芳,陈文彦.一类带有扩散的捕食模型正解的存在性[J].东南大学学报:自然科学版,2010,40(3):660-612. [doi:10.3969/j.issn.1001-0505.2010.03.042]
更新日期/Last Update: 2010-05-20