Dynamics of Kolmogorov systems of competitive type under the telegraph noise
type: Item
instance of: scholarly article
title: Dynamics of Kolmogorov systems of competitive type under the telegraph noise
zbMATH Open document ID: 1215.34064
author: Nguyen Huu Du
author: Nyuyen Hai Dang
published in: Journal of Differential Equations
publication date: 2011-01-10T00:00:00Z
review text: The authors study the dynamics of a special system of stochastic differential equations with telegraph noise and describe completely all \(\omega\)-limit sets of the solutions. Moreover, they show that the stationary distribution (if it exists) has a density and attracts all other distributions. The presented results extend important properties of this special system [see for example \textit{L. J. S. Allen}, An introduction to stochastic processes with applications to biology. Upper Saddle River, NJ: Pearson Education (2003; Zbl 1205.60001); \textit{N. H. Du, R. Kon, K. Sato} and \textit{Y. Takeuchi}, J. Comput. Appl. Math. 170, No. 2, 399--422 (2004; Zbl 1089.34047); \textit{L. J. S. Allen} and \textit{E. J. Allen}, Theor. Popul. Biol. 64, No. 4, 439--449 (2003; Zbl 1105.92023); \textit{L. Arnold, W. Horsthemke} and \textit{J. W. Stuckl}, Biom. J. 21, 451--471 (1979; Zbl 0433.92019); \textit{J. Golec} and \textit{S. Sathananthan}, Math. Comput. Modelling 38, No. 5--6, 585--593 (2003; Zbl 1052.34064); \textit{Q. Luo} and \textit{X. Mao}, J. Math. Anal. Appl. 334, No. 1, 69--84 (2007; Zbl 1113.92052)].
reviewed by: Romeo Negrea
Mathematics Subject Classification ID: 34F05
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 34C12
Mathematics Subject Classification ID: 92D25
zbMATH DE Number: 5834240
zbMATH Keywords: Kolmogorov systems of competitive type
zbMATH Keywords: telegraph noise
zbMATH Keywords: stationary distribution
zbMATH Keywords: \(\omega\)-limit set
zbMATH Keywords: competition model
MaRDI profile type: Publication
full work available at URL: j.jde.2010.08.023
OpenAlex ID: W2047316075
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DOI: 10.1016/J.JDE.2010.08.023
description: scientific article; zbMATH DE number 5834240