[1]张艳芳,陈文彦.一类捕食模型正解的存在性和惟一性[J].南京师范大学学报(自然科学版),2010,33(02):26-30.
 Zhang Yanfang,Chen Wenyan.Existence and Uniqueness of Positive Solutions for a Predator-Prey Model[J].Journal of Nanjing Normal University(Natural Science Edition),2010,33(02):26-30.
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一类捕食模型正解的存在性和惟一性()
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《南京师范大学学报》(自然科学版)[ISSN:1001-4616/CN:32-1239/N]

卷:
第33卷
期数:
2010年02期
页码:
26-30
栏目:
数学
出版日期:
2010-06-20

文章信息/Info

Title:
Existence and Uniqueness of Positive Solutions for a Predator-Prey Model
作者:
张艳芳1 陈文彦2
1. 东南大学经济管理学院, 江苏南京210018 2. 东南大学数学系, 江苏南京210018
Author(s):
Zhang Yanfang1Chen Wenyan2
1.School of Economics & Management,Southeast University,Nanjing 210018,China 2. Departm ent ofMathem atics, SoutheastUn ivers ity, Nan j ing 210018, China
关键词:
捕食模型 惟一性 存在性 反应扩散方程
Keywords:
predator-prey model uniqueness ex istence reaction-diffusion equations
分类号:
O175
摘要:
研究了一类带有修正的Holling-Ⅱ型响应函数的捕食模型的齐次Dirichlet边值问题.通过分析其相应的反应扩散系统正解的渐近性,得到了正解存在的一个必要条件,并且应用锥上的拓扑度理论指出了该条件也是正解存在的充分条件.此外,研究了一维情形下正解的惟一性.
Abstract:
A predato r-prey m ode lw ithMod ified H o lling-Type II Schemes under hom ogeneous D irich le t boundary cond-i tion is cons ide red. By analyzing the asym ptotic behav io rs of positive so lutions to the corresponding reaction-diffusion m ode,l a necessary condition fo r the ex istence o f pos itive so lutions is g iven. M o reover, by v irtue of the topo log ical deg ree theory in cones, it turns out that the necessary cond ition is suffic ient. Besides, the uniqueness o f positiv e solutions in one dim ension space is described.

参考文献/References:

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[ 5] 谭远顺, 陆炳新. 具有年龄结构的捕食系统的动力学行为[ J]. 南京师大学报: 自然科学版, 2004, 27( 1) : 13-19.
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备注/Memo

备注/Memo:
基金项目: 国家自然科学基金( 10601011) . 通讯联系人: 陈文彦, 博士, 副教授, 研究方向: 偏微分方程. E-mail:cwyseu@ 163.com
更新日期/Last Update: 2013-04-08