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一类自催化反应扩散模型共存解的分析 被引量：3

Qualitative analysis for a reaction-diffusion model with autocatalysis
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摘要 研究了带有饱和项的自催化反应扩散模型的共存解.在齐次Dirichlet边界条件下,运用度理论方法证明了系统正解的存在性.把转化率c看作分歧参数,给出了系统存在超临界和次临界分歧的条件.结果表明:转化率适当小时系统没有共存态,转化率充分大时系统一定有共存态.此外,当系统存在次临界分歧时,利用全局分歧理论可知系统至少存在两个共存态. An autocatalytic reaction-diffusion system is investigated.The coexistence states of the system is considered by using the degree theory, under the boundary conditions of Dirichlet type.Regarding the reaction rate c as the bifurcation parameter,the subcritical and supcritical bifurcations are determined.It is shown that if c is properly small,then the system has nocoexistence state,and if c is sufficiently large,then the system has at least one coexistence state.The existence of subcritical bifurcation turns out that the system has at least two coexistence states by global bifurcation theory.
作者 王治国 李艳玲
机构地区 陕西师范大学数学与信息科学学院
出处 《陕西师范大学学报（自然科学版）》 CAS CSCD 北大核心 2011年第1期10-14,共5页 Journal of Shaanxi Normal University：Natural Science Edition
基金 国家自然科学基金资助项目(10971124) 国家自然科学基金青年资助项目(10902062) 教育部高等学校博士点专项科研基金项目(200807180004) 陕西省自然科学基础研究计划项目(2009JQ1007)
关键词 自催化 分歧 反应扩散模型 autocatalytic bifurcation reaction-diffusion model
分类号 O175.26 [理学—基础数学]
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参考文献8

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同被引文献25

  • 1李大华.一类食物链模型的周期解的二级分歧[J].数学物理学报（A辑）,1992,12(S1):138-139. 被引量：1
  • 2Ko W,Ryu K.Qualitative analysis of a predator-prey model with Holling type ⅡI functional response incorporating a prey refuge[J].Journal of Differential Equations,2006,231 (2):534-550.
  • 3Peng Rui,Shi Junping.Non-existence of non-constant positive steady states of two Holling type-Ⅱ predator prey systems:Strong interaction case[J].Journal of Differential Equations,2009,247:866-886.
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  • 5Dancer E N.On the indices of fixed points of mapping in cones and applications[J].Journal of Mathematical Analysis and Applications,1983,91(1):131-151.
  • 6Dancer E N,Du Yihong.Positive solutions for a threespecies competition system with diffusion-Ⅰ.General existence results[J].Nonlinear Analysis:Theory,Methods and Applications,1995,24(3):337-357.
  • 7Zheng Sining,Liu Jing.Coexistence solutions for a reaction-diffusion system of un-stirred chemostat model[J].Applied Mathematics and Computation,2003,145(3):597-590.
  • 8王明新.非线性椭圆型方程[M].北京:科学出版社,2003:141.
  • 9Brown K J. Nontrivial solutions of predator-prey systems with small diffusion[J].{H}Nonlinear Analysis TMA,1987.685-689.
  • 10Conway E D,Gardner R,Smoller J. Stability and bifurcation of steady-state solutions for predator-prey equations[J].{H}ADVANCES IN APPLIED MATHEMATICS,1982,(3):288-334.

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陕西师范大学学报（自然科学版）
2011年 第1期

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