Population dynamical behavior of non-autonomous Lotka-Volterra competitive system with random perturbation

X. Li; X. Mao; National Natural Science Foundation of China (Funder); Key Project of Chinese Ministry of Education (Funder); Key Laboratory for Applied Statistics of MOE (KLAS) (Funder)

doi:10.3934/dcds.2009.24.523

Population dynamical behavior of non-autonomous Lotka-Volterra competitive system with random perturbation

X. Li, X. Mao, National Natural Science Foundation of China (Funder), Key Project of Chinese Ministry of Education (Funder), Key Laboratory for Applied Statistics of MOE (KLAS) (Funder)

Mathematics And Statistics

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Abstract

In this paper, we consider a non-autonomous stochastic Lotka-Volterra competitive system dxi(t) = xi(t)[(bi(t)¡ nPj=1aij (t)xj (t))dt+¾i(t)dBi(t)], where Bi(t) (i = 1; 2; ¢ ¢ ¢ ; n) are independent standard Brownian motions. Some dynamical properties are discussed and the su±cient conditions for the existence of global positive solutions, stochastic permanence, extinction as well as global attractivity are obtained. In addition, the limit of the average in time of the sample paths of solutions is estimated.

Original language	English
Pages (from-to)	523-593
Number of pages	70
Journal	Discrete and Continuous Dynamical Systems - Series A
Volume	24
Issue number	2
DOIs	https://doi.org/10.3934/dcds.2009.24.523
Publication status	Published - 2009

Keywords

brownian motion
stochastic di®erential equation
It^o's formula
stochastic permanence
global attractivity

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Li, X., Mao, X., National Natural Science Foundation of China (Funder), Key Project of Chinese Ministry of Education (Funder), & Key Laboratory for Applied Statistics of MOE (KLAS) (Funder) (2009). Population dynamical behavior of non-autonomous Lotka-Volterra competitive system with random perturbation. Discrete and Continuous Dynamical Systems - Series A, 24(2), 523-593. https://doi.org/10.3934/dcds.2009.24.523

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title = "Population dynamical behavior of non-autonomous Lotka-Volterra competitive system with random perturbation",

abstract = "In this paper, we consider a non-autonomous stochastic Lotka-Volterra competitive system dxi(t) = xi(t)[(bi(t)¡ nPj=1aij (t)xj (t))dt+¾i(t)dBi(t)], where Bi(t) (i = 1; 2; ¢ ¢ ¢ ; n) are independent standard Brownian motions. Some dynamical properties are discussed and the su±cient conditions for the existence of global positive solutions, stochastic permanence, extinction as well as global attractivity are obtained. In addition, the limit of the average in time of the sample paths of solutions is estimated.",

keywords = "brownian motion, stochastic di{\textregistered}erential equation, It\textasciicircum{}o's formula, stochastic permanence, global attractivity",

author = "X. Li and X. Mao and \{National Natural Science Foundation of China (Funder)\} and \{Key Project of Chinese Ministry of Education (Funder)\} and \{Key Laboratory for Applied Statistics of MOE (KLAS) (Funder)\}",

year = "2009",

doi = "10.3934/dcds.2009.24.523",

language = "English",

volume = "24",

pages = "523--593",

journal = "Discrete and Continuous Dynamical Systems - Series A",

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publisher = "American Institute of Mathematical Sciences",

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Li, X, Mao, X, National Natural Science Foundation of China (Funder), Key Project of Chinese Ministry of Education (Funder) & Key Laboratory for Applied Statistics of MOE (KLAS) (Funder) 2009, 'Population dynamical behavior of non-autonomous Lotka-Volterra competitive system with random perturbation', Discrete and Continuous Dynamical Systems - Series A, vol. 24, no. 2, pp. 523-593. https://doi.org/10.3934/dcds.2009.24.523

TY - JOUR

T1 - Population dynamical behavior of non-autonomous Lotka-Volterra competitive system with random perturbation

AU - Li, X.

AU - Mao, X.

AU - National Natural Science Foundation of China (Funder)

AU - Key Project of Chinese Ministry of Education (Funder)

AU - Key Laboratory for Applied Statistics of MOE (KLAS) (Funder)

PY - 2009

Y1 - 2009

N2 - In this paper, we consider a non-autonomous stochastic Lotka-Volterra competitive system dxi(t) = xi(t)[(bi(t)¡ nPj=1aij (t)xj (t))dt+¾i(t)dBi(t)], where Bi(t) (i = 1; 2; ¢ ¢ ¢ ; n) are independent standard Brownian motions. Some dynamical properties are discussed and the su±cient conditions for the existence of global positive solutions, stochastic permanence, extinction as well as global attractivity are obtained. In addition, the limit of the average in time of the sample paths of solutions is estimated.

AB - In this paper, we consider a non-autonomous stochastic Lotka-Volterra competitive system dxi(t) = xi(t)[(bi(t)¡ nPj=1aij (t)xj (t))dt+¾i(t)dBi(t)], where Bi(t) (i = 1; 2; ¢ ¢ ¢ ; n) are independent standard Brownian motions. Some dynamical properties are discussed and the su±cient conditions for the existence of global positive solutions, stochastic permanence, extinction as well as global attractivity are obtained. In addition, the limit of the average in time of the sample paths of solutions is estimated.

KW - brownian motion

KW - stochastic di®erential equation

KW - It^o's formula

KW - stochastic permanence

KW - global attractivity

U2 - 10.3934/dcds.2009.24.523

DO - 10.3934/dcds.2009.24.523

M3 - Article

SN - 1078-0947

VL - 24

SP - 523

EP - 593

JO - Discrete and Continuous Dynamical Systems - Series A

JF - Discrete and Continuous Dynamical Systems - Series A

IS - 2

ER -

Li X, Mao X, National Natural Science Foundation of China (Funder), Key Project of Chinese Ministry of Education (Funder), Key Laboratory for Applied Statistics of MOE (KLAS) (Funder). Population dynamical behavior of non-autonomous Lotka-Volterra competitive system with random perturbation. Discrete and Continuous Dynamical Systems - Series A. 2009;24(2):523-593. doi: 10.3934/dcds.2009.24.523

Population dynamical behavior of non-autonomous Lotka-Volterra competitive system with random perturbation

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