[1]张艳芳,陈文彦.一类捕食模型正解的唯一性和稳定性[J].东南大学学报(自然科学版),2010,40(4):882-884.[doi:10.3969/j.issn.1001-0505.2010.04.041]
 Zhang Yanfang,Chen Wenyan.Uniqueness and stability of positive solutions to a predator-prey model[J].Journal of Southeast University (Natural Science Edition),2010,40(4):882-884.[doi:10.3969/j.issn.1001-0505.2010.04.041]
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一类捕食模型正解的唯一性和稳定性()
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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4期
页码:
882-884
栏目:
数学、物理学、力学
出版日期:
2010-07-20

文章信息/Info

Title:
Uniqueness and stability of positive solutions to a predator-prey model
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:
捕食模型 唯一性 稳定性 隐函数定理
Keywords:
predator-prey model uniqueness existence implicit function theorem
分类号:
O175.25
DOI:
10.3969/j.issn.1001-0505.2010.04.041
摘要:
讨论了一类具有饱和与竞争项的捕食模型,其中边界条件为齐次Dirichlet边界条件.主要分析了当竞争系数充分大时正解的性质.首先,利用标准的正则性理论和嵌入定理,得到了正解的渐近性.其次,利用隐函数定理推导出正解的唯一性.最后,结合线性化稳定性理论得到正解的稳定性.结果表明,猎物之间的强竞争限制了种群的多样性,并导致2种群的捕食系统更加稳定.
Abstract:
A predator-prey model with predator saturation and competition under homogeneous Dirichlet boundary condition is discussed.The property of positive solutions is mainly concerned when the competitive parameter is large enough. Firstly, using the standard regularity theory and embedding theorem, the asymptotic behavior of positive solutions is given. Secondly, by virtue of the implicit function theorem the uniqueness is investigated. Moreover, the stability is obtained using the linear stability theory. It turns out that the species diversity is limited and the predatory system is more stable when the interference between the predator species is strong.

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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.一类捕食模型正解的唯一性和稳定性[J].东南大学学报:自然科学版,2010,40(4):882-884. [doi:10.3969/j.issn.1001-0505.2010.04.041]
更新日期/Last Update: 2010-07-20