[1]谢溪庄.具有阶段结构和非局部空间效应的竞争系统的稳定性[J].华侨大学学报(自然科学版),2012,33(6):715-720.[doi:10.11830/ISSN.1000-5013.2012.06.0715]
　XIE Xi-zhuang.Stability in Competition Models with Stage Structure and Nonlocal Spatial Effect[J].Journal of Huaqiao University(Natural Science),2012,33(6):715-720.[doi:10.11830/ISSN.1000-5013.2012.06.0715]
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具有阶段结构和非局部空间效应的竞争系统的稳定性()
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《华侨大学学报（自然科学版）》[ISSN:1000-5013/CN:35-1079/N]

卷:
第33卷
期数:
2012年第6期
页码:
715-720
栏目:
出版日期:
2012-11-20

文章信息/Info

Title:
Stability in Competition Models with Stage Structure and Nonlocal Spatial Effect
文章编号:
1000-5013(2012)06-0715-06
作者:
谢溪庄
华侨大学 数学科学学院, 福建 泉州 362021
Author(s):
XIE Xi-zhuang
School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China
关键词:
阶段结构;  非局部空间效应;  反应扩散模型;  稳定性
Keywords:
stage structure;  nonlocal spatial effect;  reaction-diffusion model;  stability
分类号:
O175.2
DOI:
10.11830/ISSN.1000-5013.2012.06.0715
文献标志码:
A
摘要:
构造一类具有阶段结构和非局部空间效应影响的两种成年种群个体相互竞争的反应扩散模型.利用线性稳定化方法和Redlinger上下解方法得到该竞争模型的动力性态,并证明模型在边界平衡点和共存平衡点是全局渐近稳定的.
Abstract:
In this paper, the author constructs a reaction-diffusion model with stage structure and nonlocal spatial effect, the models with the interaction between the two species and adult members in which are in competition. By using the method of upper-lower solutions due to Redlinger, dynamical behaviors of model are studied. Sharp global stability criteria are established for the coexistence equilibrium as well as the extinction equilibrium.

参考文献/References:

[1] XU Rui,CHAPLAIN A J,DAVIDSON F A.Traveling wave and convergence in stagestructured reaction diffusion competitive models with nonlocal delays[J].Chaos Solitons and Fractals,2006,30(4):974-992.
[2] LIU S Q,CHEN L S,LUO G L,et al.Asymptotic behaviors of competitive Lotka-Volterra system with stage Structure[J].J Math Anal Appl,2002,271(1):124-38.
[3] 谢溪庄,刘胜强,白正简.具有非线性种内制约关系和阶段结构的竞争系统研究[D].厦门:厦门大学,2008.
[4] GILPIN M.AYALA F.Global Models of Growth and Competition[J].Proc Nat Acad Sci USA,1973,70(12):3590-3593.
[5] REDLINGER R.Existence theorems for semilinear parabolic systems with functionals[J].Nonlinear Anal TMA,1984,8(6):667-682.
[6] BRITTON N F.Reaction-diffusion equations and their applications to biology[M].New York:Academic,1986.
[7] GUURLEY S A,KUANG Y.Wavefronts and global stability in a time delayed population model with stage structure[J].Proc Roy Soc Lond A,2003,459(2034):1563-1579.
[8] AL-OMARI J F M,GOURLEY S A.Stability and traveling fronts in Lotka-Vloterra competition models with stage structure[J].SIAM J Appl Math,2003,63(6):2063-2086.

备注/Memo

备注/Memo:
收稿日期: 2011-10-29
通信作者: 谢溪庄(1981-),男,助教,主要从事生物数学的研究.E-mail:xzx@hqu.edu.cn.
基金项目: 国务院侨办科研基金资助项目(09QZR10)
更新日期/Last Update: 2012-11-20