Generalized stochastic delay Lotka-Volterra systems

X. Mao, J. Yin, F. Wu

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

This article deals with a class of generalized stochastic delay Lotka-Volterra systems of the form dX(t) = diag(X1(t), X2(t),..., Xn(t))[(f(X(t)) + g(X(t - τ)))dt + h(X(t))dB(t)]. Under some unrestrictive conditions on f, g, and h, we show that the unique solution of such a stochastic system is positive and does not explode in a finite time with probability one. We also establish some asymptotic boundedness results of the solution including the time average of its (β + )-order moment, as well as its asymptotic pathwise estimation. As a by-product, a stochastic ultimate boundedness of the solution for this stochastic system is directly derived. Three examples are given to illustrate our conclusions.
LanguageEnglish
Pages436-454
Number of pages18
JournalStochastic Models
Volume25
Issue number3
DOIs
Publication statusPublished - 2009

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Lotka-Volterra System
Stochastic systems
Delay Systems
Stochastic Systems
Ultimate Boundedness
Time-average
Unique Solution
Byproducts
Boundedness
Moment
Form
Class

Keywords

  • asymptotic boundedness of moment
  • brownian motion
  • lotka-volterra model
  • stochastic delay differential equation
  • stochastic ultimate boundedness

Cite this

Mao, X. ; Yin, J. ; Wu, F. / Generalized stochastic delay Lotka-Volterra systems. In: Stochastic Models. 2009 ; Vol. 25, No. 3. pp. 436-454.
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Generalized stochastic delay Lotka-Volterra systems. / Mao, X.; Yin, J.; Wu, F.

In: Stochastic Models, Vol. 25, No. 3, 2009, p. 436-454.

Research output: Contribution to journalArticle

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T1 - Generalized stochastic delay Lotka-Volterra systems

AU - Mao, X.

AU - Yin, J.

AU - Wu, F.

PY - 2009

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AB - This article deals with a class of generalized stochastic delay Lotka-Volterra systems of the form dX(t) = diag(X1(t), X2(t),..., Xn(t))[(f(X(t)) + g(X(t - τ)))dt + h(X(t))dB(t)]. Under some unrestrictive conditions on f, g, and h, we show that the unique solution of such a stochastic system is positive and does not explode in a finite time with probability one. We also establish some asymptotic boundedness results of the solution including the time average of its (β + )-order moment, as well as its asymptotic pathwise estimation. As a by-product, a stochastic ultimate boundedness of the solution for this stochastic system is directly derived. Three examples are given to illustrate our conclusions.

KW - asymptotic boundedness of moment

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