Asymptotic behavior of predator-prey systems perturbed by white noise

Nguyen Hai Dang; Nguyen Huu Du; Ta Viet Ton

doi:10.1007/s10440-011-9628-4

Asymptotic behavior of predator-prey systems perturbed by white noise

Nguyen Hai Dang, Nguyen Huu Du, Ta Viet Ton

Research output: Contribution to journal › Article › peer-review

14 Citations (Scopus)

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 L¹ to an invariant density or converges weakly to a singular measure on the boundary.

Original language	English
Pages (from-to)	351-370
Number of pages	20
Journal	Acta Applicandae Mathematicae
Volume	115
Issue number	3
DOIs	https://doi.org/10.1007/s10440-011-9628-4
Publication status	Published - Sept 2011
Externally published	Yes

All Science Journal Classification (ASJC) codes

Applied Mathematics

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10.1007/s10440-011-9628-4

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AU - Ton, Ta Viet

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AB - 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 L1 to an invariant density or converges weakly to a singular measure on the boundary.

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Asymptotic behavior of predator-prey systems perturbed by white noise

Abstract

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