[1]张艳芳,陈文彦.一类捕食模型正解的存在性和惟一性[J].南京师大学报(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.
点击复制

一类捕食模型正解的存在性和惟一性()
分享到：

《南京师大学报（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 Yanfang1; Chen 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 mode; l 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:

[ 1] Bazykin A D. Non linear Dynam ics o f Interacting Popu la tions[M ]. Singapo re: W o rld Scien tific, 1998.
[ 2] W ang M X, Wu Q. Pos itive so lutions of a prey-predato rm odelw ith preda tor saturation and com petition[ J]. JM ath AnalApp, l 2008, 345( 2): 708-718.
[ 3] ChenW Y, W angM X. Qua lita tive ana lysis o f predator-prey models w ith Bedd ing ton-Deange lis func tiona l responses and d i-f fus ion[ J] . M ath CompM ode lling, 2005, 42( 1 /2) : 31-44.
[ 4] 陈滨, 王明新. 带有扩散和Bedding ton-Deange lis型响应函数的捕食模型的正平衡态[ J]. 数学年刊( A 辑), 2007, 28 ( 4): 495-506.
[ 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.
[ 6] Pao C V. Nonlinear Pa rabo lic and E llip tic Equations[M ]. New York: Plenum Press, 1992.
[ 7] DelgadoM, L?pez-G?m ez J, Sua rez A. On the symb io tic Lo tka-Vo lterramodel w ith d iffus ion and transport effects[ J] . J D i-f ferential Equa tions, 2000, 160( 1): 321-349.
[ 8] L?pez-G?m ez J, Pardo R M. Ex istence and uniqueness o f coex istence states fo r the predator-preym ode lw ith d iffus ion in the sca lar case[ J]. Ex tractaM ath, 1991, 6( 2): 115-118.

相似文献/References:

[1]吴凤芹,徐焱.关于亚纯函数及其导函数弱权分担小函数的惟一性[J].南京师大学报(自然科学版),2010,33(01):32.
　Wu Fengqin,Xu Yan.Uniqueness of Meromorphic Functions Weakly Weighted-Sharing One Small Function With Their Derivatives[J].Journal of Nanjing Normal University(Natural Science Edition),2010,33(02):32.
[2]朱颖中,常建明.与导数分担有理函数的整函数[J].南京师大学报(自然科学版),2008,31(03):44.
　Zhu Yingzhong,Chang Jianming.On Entire Functions That Share a Rational Function With Their Derivatives[J].Journal of Nanjing Normal University(Natural Science Edition),2008,31(02):44.
[3]仇惠玲.分担有理函数的亚纯函数(英文)[J].南京师大学报(自然科学版),2007,30(01):6.
　Qiu Huiling.Meromorphic Functions That Share Rational Functions[J].Journal of Nanjing Normal University(Natural Science Edition),2007,30(02):6.
[4]仇惠玲.关于Gross问题的一个结果[J].南京师大学报(自然科学版),2004,27(02):10.
　Qiu Huiling.A Result on a Problem of Gross[J].Journal of Nanjing Normal University(Natural Science Edition),2004,27(02):10.

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