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一类四维竞争系统的动力学 被引量：2

Dynamics of a Kind of Four-Dimensional Competitive System
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摘要 研究了有不变超平面的四维竞争Lotka-Volterra系统的动力学性态:平衡点的存在性和局部稳定性、不变超平面的全局稳定性,还讨论了被限定在不变超平面上的三维等价系统的一些动力学.通过研究发现了下列结论:这类模型不存在孤立的四竞争者或二竞争者共存平衡点、至多有两个孤立的三竞争者共存的平衡点、不变超平面是全局渐近吸引的、竞争的限定系统只有两种等价类等结论. This paper studies dynamical behaviors of four-dimensional competitive Lotka-Volterra system with an invariant hyperplane including existence and local stability of all equilibriums, global stability of the invariant hyperplane. It also discusses dynamics of three-dimensional equivalent system when it is restricted in the invariant hyperplane. Through research, the results can be found such as isolated equilibrium with four or two competitors living being not exist, existence of at most two isolated equilibriums with three competitors living, the invariant hyperplane being global asymptotic attractor, competitive restricted system only being divided into two classes.
作者 王瑞平 丁剑平
机构地区 上海财经大学金融学院
出处 《河南大学学报（自然科学版）》 CAS 北大核心 2014年第2期137-140,共4页 Journal of Henan University:Natural Science
基金 国家自然科学基金资助项目(11271252)
关键词 平衡点 不变超平面 LOTKA-VOLTERRA系统 竞争Lotka-Volterra系统 全局渐近吸引 equilibrium invariant hyperplane Lotka-Volterra system competitive Lotka-Volterra system globalasymptotic attractor
分类号 O175.13 [理学—基础数学]
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参考文献19

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二级参考文献13

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共引文献2

同被引文献17

  • 1ZEEMAN E C,ZEEMAN M L.An n-dimensional competitive Lotka-Volterra system is generically determined by the edges of its carrying simplex[J].Nonlinearity,2002,15(3):2019-2032.
  • 2WANG R P,XIAO D M.Bifurcations and chaotic dynamics in a 4-dimensional competitive Lotka-Volterra system[J].Nonlinear Dynamics,2010,59(3):411-422.
  • 3ALY S.Competition in patchy space with cross-diffusion and toxic substances[J].Nonlinear Analysis:Real World Applications,2009,10(1):185-190.
  • 4ALY S,FARKAS M.Competition in patchy environment with cross diffusion[J].Nonlinear Analysis:Real World Applications,2004,5(4):589-595.
  • 5WANG R P.Competition in a patchy environment with cross-diffusion in a 3-dimensional Lotka-Volterra system[J].Nonlinear Analysis:Real World Applications,2010,11(4):2726-2730.
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  • 8CAI L M,SONG X Y.Permanence and stability of a predator-prey system with stage structure for predator[J].Appl Math Comput,2007,201:356-366.
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  • 10KUANG Y.Delay differential equations with application in population dynamics[J].Academic Press,1993(1):163-166.

引证文献2

二级引证文献3

河南大学学报（自然科学版）
2014年 第2期

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