Tohoku Mathematical Journal

The evolution of periodic population systems under random environments

Ryusuke Kon, Huu Du Nguyen, Kazunori Sato, and Yasuhiro Takeuchi

Full-text: Open access

Abstract

In this paper we study the behavior of trajectories of the Lotka-Volterra competition system with periodic coefficients under telegraph noise. We give sufficient conditions for the average permanence. Furthermore, we determine the $\omega$-limit sets of the system.

Article information

Source
Tohoku Math. J. (2), Volume 57, Number 4 (2005), 447-468.

Dates
First available in Project Euclid: 23 February 2006

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1140727068

Digital Object Identifier
doi:10.2748/tmj/1140727068

Mathematical Reviews number (MathSciNet)
MR2203542

Zentralblatt MATH identifier
1117.34052

Subjects
Primary: 34C12: Monotone systems
Secondary: 60H10: Stochastic ordinary differential equations [See also 34F05] 92D25: Population dynamics (general)

Keywords
Lotka-Volterra equation competition bistable telegraph noise average permanence

Citation

Nguyen, Huu Du; Kon, Ryusuke; Sato, Kazunori; Takeuchi, Yasuhiro. The evolution of periodic population systems under random environments. Tohoku Math. J. (2) 57 (2005), no. 4, 447--468. doi:10.2748/tmj/1140727068. https://projecteuclid.org/euclid.tmj/1140727068


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