期刊文献+
任意字段
题名或关键词
题名
关键词
文摘
作者
第一作者
机构
刊名
分类号
参考文献
作者简介
基金资助
栏目信息

一类时滞和阶段结构食物链系统的局部分析

Local analysis of a food-chain model with stage structure and time delay
下载PDF
导出
摘要 对一类3种群的捕食被捕食模型,运用上下解方法、正性引理和线性化方法,研究了具有时滞和阶段结构弱耦合半线性抛物方程组的存在性和渐近性态.获得了解的整体存在惟一性,并给出了非平凡平衡解局部渐近稳定性易验证的充分条件. A three-species predator-prey model was discussed. By means of the methods of upper-lower solutions ,the positive lemma and linearization, the existence and asymptotic behaviorus of weak coupled system of semi-linear parabolic equations with time delay and stage structure were studied. The global existence-uniqueness of solutions is obtained and the easy verifiable sufficient conditions for local asymptotic stability of a non-trivial steady-state solutions are given
作者 苗宝军 容跃堂 周伦
机构地区 西安工程大学理学院 许昌学院数学科学学院
出处 《纺织高校基础科学学报》 CAS 2008年第2期182-187,共6页 Basic Sciences Journal of Textile Universities
基金 西安工程大学校管基金资助项目(2007XG28) 河南省科技厅自然科学基金资助项目(0611055100) 河南省教育自然科学基础研究项目(2006120006)
关键词 捕食被捕食 反应扩散系统 局部渐近稳定 阶段结构 上下解 时滞 predator-prey reaction-diffusion system local asymptotic stability stage structure upper and lower solutions time delay
分类号 O175.26 [理学—基础数学]
  • 相关文献

参考文献11

  • 1TENG Z D. Permance and stability of Lotka-Volterra type N-species competitive system[J]. Acta Mathematica Sinica: Chinese Series,2002,45(5) : 905-918.
  • 2PAO C V. Nonlinear parabolic and elliptic equations[M]. New York, London: Plenum, 1992.
  • 3高海燕,伏升茂.带交错扩散项的捕食者-食饵模型的整体解[J].纺织高校基础科学学报,2006,19(3):236-240. 被引量：2
  • 4OU L M, LUO G L, YANG Y L, The asymptotic behaviors of a stage-structured autonomous predator-prey system with time delay[J]. J Math Anal Appl,2003,283: 534-548.
  • 5CUI J,SONG X. Permanence of predator-prey system with stage structure[J]. Discrete Contin Dyn Syst Ser B,2004, 4:547-554.
  • 6ZHANG X, CHEN L, NEUMANN A U. The stage-structured predator-prey model and optimal harvesting policy [J]. Math Biosci, 2000,168: 201-210.
  • 7LIU S Q,CHEN L S,LUO G L. Asymptotic behaviors of competive Lotka- Volterra system with stage structure[J].J Math Anal Appl, 2002,271 : 124-138.
  • 8JIANG D Q, Zhang L L. Positive solutions for boundary value problem of second-order delay differential equations [J]. Acta Mathematica Sinica: Chinese Series, 2003,46 (4) : 739-746.
  • 9WANG M X. Non-constant positive steady-state of the sel'kov model[J]. J Differential Equations, 2003,190.. 600- 620.
  • 10XD F, HOU Y,LIN Z G. Time delay parabolic system in a predator-prey model with stage structure[J]. Acta Mathematica Sinica:Chinese Series,2005,48(6):1 121-1 130.

二级参考文献10

  • 1SHIGESADA N,KAWASAKI K,TERAMOTO E.Spatial segregation of interacting species[J].J Theoret Biol,1979,79:83-99.
  • 2KUTO K.Stability of steady-state solutions to a prey-predator system with cross-diffusion[J].J Diff Eqs,2004,197:293-314.
  • 3KUTO K,YAMADA Y.Multiple coexistence states for a prey-predator system with cross-diffusion[J].J Diff Eqs,2004,197:315-348.
  • 4SEONG-A SHIM.Uniform boundedness and convergence of solutions to cross-diffusion systems[J].J Diff Eqs,2002,185:281-305.
  • 5GALIAMO G,JNGEL A,GARZN M.Semi-discretization in time and numerical convergence of a non-linear cross-diffusion population model[J].Numer Math,2003,93:655-673.
  • 6CHOI Y S,LUI R,YAMADA Y.Existence of global solutions for the Shigesada-Kawasaki-Teramoto model with weak cross-diffusion[J].Discrete and Continuous Dynamical systems,2003(9):1 193-1 200.
  • 7PANG P Y H,WANG MINGXIN.Strategy and stationary pattern in a three-species predator-prey model[J].J Diff Eqs,2004,200:245-273.
  • 8AMANN H.Dynamic theory of quasilinear parabolic equations-Ⅰ.Abstract evolution equation[J].Nonlinear Analysis,1988(12):859-919.
  • 9AMANN H.Dynamic theory of quasilinear parabolic equation -Ⅱ.Reaction-diffusion[J].Diff Int Eqs,1990(3):13-75.
  • 10AMANN H.Dynamic theory of quasilinear parabolic equations-Ⅲ.Global existence[J].Math Z,1989,202:219-250.

共引文献1

纺织高校基础科学学报
2008年 第2期

相关作者

内容加载中请稍等...

相关机构

内容加载中请稍等...

相关主题

内容加载中请稍等...

浏览历史

内容加载中请稍等...
;
使用帮助 返回顶部