Mao, X. and Yin, J. and Wu, F. (2009) *Generalized stochastic delay Lotka-Volterra systems.* Stochastic Models, 25 (3). pp. 436-454. ISSN 1532-6349

## 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.

Item type: | Article |
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ID code: | 14054 |

Keywords: | asymptotic boundedness of moment, brownian motion, lotka-volterra model, stochastic delay differential equation, stochastic ultimate boundedness, Mathematics, Modelling and Simulation, Applied Mathematics, Statistics and Probability |

Subjects: | Science > Mathematics |

Department: | Faculty of Science > Mathematics and Statistics |

Related URLs: | |

Depositing user: | Mrs Carolynne Westwood |

Date Deposited: | 11 Jan 2010 16:56 |

Last modified: | 04 Sep 2014 23:21 |

URI: | http://strathprints.strath.ac.uk/id/eprint/14054 |

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