## Tohoku Mathematical Journal 2005 December SECOND SERIES VOL. 57, NO. 4

 Tohoku Math. J. 57 (2005), 447-468

Title THE EVOLUTION OF PERIODIC POPULATION SYSTEMS UNDER RANDOM ENVIRONMENTS

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

(Received March 4, 2003, revised May 11, 2005)
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.

2000 Mathematics Subject Classification. Primary 34C12; Secondary 60H10, 92D25.

Key words and phrases. Lotka-Volterra equation, competition, bistable, telegraph noise, average permanence.