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)

Research output: Contribution to journalArticle

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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.
LanguageEnglish
Pages523-593
Number of pages70
JournalDiscrete and Continuous Dynamical Systems - Series A
Volume24
Issue number2
DOIs
Publication statusPublished - 2009

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Competitive System
Random Perturbation
Lotka-Volterra System
Brownian movement
Dynamical Behavior
Global Attractivity
Permanence
Sample Path
Extinction
Brownian motion
Positive Solution
Standards

Keywords

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

Cite this

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
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. In: Discrete and Continuous Dynamical Systems - Series A. 2009 ; Vol. 24, No. 2. pp. 523-593.
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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

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

In: Discrete and Continuous Dynamical Systems - Series A, Vol. 24, No. 2, 2009, p. 523-593.

Research output: Contribution to journalArticle

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

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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.

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KW - stochastic di®erential equation

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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). 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. https://doi.org/10.3934/dcds.2009.24.523