Uniform persistence for nonautonomous and random parabolic Kolmogorov systems
- 作者：Mierczynski ; Janusz ; Shen ; Wenxian ; Zhao ; Xiao-Qiang
- 关键词：35B41 ; 35K55 ; 37B55 ; 37H15 ; 37L55 ; 92D25 ; Uniform persistence ; Nonautonomous/random systems ; Skew-product semiflows ; Principal spectrum ; Lyapunov exponents ; Unsaturated invariant set ; Random equilibrium
- 刊名：Journal of Differential Equations
- 出版年：2004
- 期刊代码：74_00220396
- 类别：mt
- 出版时间：September 20, 2004
- 卷：204
- 期：2
- 页码：471-510
- 文件大小：453 K
摘要
The purpose of this paper is to investigate uniform persistence for nonautonomous and random parabolic Kolmogorov systems via the skew-product semiflows approach. It is first shown that the uniform persistence of the skew-product semiflow associated with a nonautonomous (random) parabolic Kolmogorov system implies that of the system. Various sufficient conditions in terms of the so-called unsaturatedness and/or Lyapunov exponents for uniform persistence of the skew-product semiflows are then provided. Among others, it is shown that if the associated skew-product semiflow has a global attractor and its restriction to the boundary of the state space has a Morse decomposition which is unsaturated or whose external Lyapunov exponents are positive, then it is uniformly persistent. More specific conditions are discussed for uniform persistence in n-species, particularly 3-species, random competitive systems.