Asymptotic Behavior of Predator-Prey Systems Perturbed by White Noise

Authors: Dang, Nguyen1; Du, Nguyen2; Ton, Ta3

Source: Acta Applicandae Mathematicae, Volume 115, Number 3, September 2011 , pp. 351-370(20)

Publisher: Springer

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Abstract:

In this paper, we develop the results in Rudnicki (Stoch. Process. Appl. 108:93–107, 2003) to a stochastic predator-prey system where the random factor acts on the coefficients of environment. We show that there exists the density functions of the solutions and then, study the asymptotic behavior of these densities. It is proved that the densities either converges in L 1 to an invariant density or converges weakly to a singular measure on the boundary.

Keywords: 34C12; 47D07; 60H10; 92D25; Asymptotic stability; Diffusion process; Markov semigroups; Prey-predator model

Document Type: Research Article

DOI: http://dx.doi.org/10.1007/s10440-011-9628-4

Affiliations: 1: Faculty of Mathematics, Mechanics and Informatics, Hanoi University of Science, Hanoi, Vietnam 2: Faculty of Mathematics, Mechanics and Informatics, Hanoi University of Science, Hanoi, Vietnam, Email: dunh@vnu.edu.vn 3: Department of Applied Physics, Graduate School of Engineering, Osaka University, Osaka, Japan

Publication date: September 1, 2011

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