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Journal of Evolution Equations

, Volume 4, Issue 3, pp 371–390 | Cite as

Lyapunov exponents and asymptotic dynamics in random Kolmogorov models

  • Janusz MierczyńskiEmail author
  • Wenxian Shen
Original Paper

Abstract.

The current paper is devoted to the investigation of asymptotic dynamics in random Kolmogorov models. Applying the theory of principal Lyapunov exponents and the principal spectrum developed in the authors’ previous papers together with the concept of part metric it provides conditions for the existence of a globally attracting positive random equilibrium, the existence of a globally attracting uniformly positive random equilibrium, and the extinction in random Kolmogorov models. These results are an important complement to the existing ones.

2000 Mathematics Subject Classification:

35B40 35K10 35P05 37B55 37H15 37L55 92D25. 

Key words:

Lyapunov exponent exponential separation principal spectrum random Kolmogorov models positive random equilibrium uniformly extinction. 

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Copyright information

© Birkhäuser Verlag, Basel 2004

Authors and Affiliations

  1. 1.Institute of MathematicsWrocław University of TechnologyWrocławPoland
  2. 2.Department of MathematicsAuburn UniversityAuburnUSA

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