上海交通大学学报

上海交通大学学报（自然版）

• 数学 • 上一篇    下一篇

两地间的三维竞争LotkaVolterra系统中的分岔

王瑞平   

  1. (上海交通大学 理学院， 上海 200240)
  • 收稿日期:2009-07-05 修回日期:1900-01-01 出版日期:2010-06-30 发布日期:2010-06-30

Bifurcations in Threedimensional Competitive LotkaVolterra System Living in Two Patchy Environment

WANG Ruiping   

  1. (Department of Mathematics, Shanghai Jiaotong University, Shanghai 200240, China)
  • Received:2009-07-05 Revised:1900-01-01 Online:2010-06-30 Published:2010-06-30

摘要： 主要研究了在两地间的三维竞争LotkaVolterra系统中由交错扩散引起的分岔.当两地间无扩散时，给出了三维竞争LotkaVolterra系统的3种群共存的不动点渐近稳定的条件；当两地间出现扩散时，给出了发生Hopf分岔和静态分岔的临界条件并且给出了具体的例子.研究表明，交错迁移反应是非常重要而不应该被忽视的因子.

关键词: 分岔, Hopf 分岔, 静态分岔, 竞争LotkaVolterra系统, 交错扩散

Abstract: This paper, studied bifurcations in threedimensional competitive LotkaVolterra system living in two patchy environments. It is studied about asymptotical stability of equilibrium with threespecies alive when there is no crossdiffusion within the two patchy. And, there are some different critical values of the bifurcation parameter at which the system undergoes Hopf bifurcation, static bifurcation respectively under the effect of crossdiffusion. Some examples were also given. This illustrates the crossmigration response is very important factor that should not be ignored.

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