Stochastic delay Lotka-Volterra model

Bahar, Arifah and Mao, Xuerong (2004) Stochastic delay Lotka-Volterra model. Journal of Mathematical Analysis and Applications, 292 (2). pp. 364-380. ISSN 0022-247X

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    Abstract

    We reveal in this paper that the environmental noise will not only suppress a potential population explosion in the stochastic delay Lotka-Volterra model but will also make the solutions to be stochastically ultimately bounded. To reveal these interesting facts, we stochastically perturb the delay Lotka-Volterra model ̇ x(t) = diag(x1 (t),..., xn(t))[b + Ax(t - τ)] into the Itô form dx(t) = diag(x1 (t),..., xn(t) [(b + Ax(t - τ))dt + σ x(t) dw(t)], and show that although the solution to the original delay equation may explode to infinity in a finite time, with probability one that of the associated stochastic delay equation does not. We also show that the solution of the stochastic equation will be stochastically ultimately bounded without any additional condition on the matrix A.

    Author(s):Bahar, Arifah and Mao, Xuerong ORCID logoORCID: https://orcid.org/0000-0002-6768-9864
    Item type:Article
    ID code:55864
    Keywords:Brownian motion, explosion, Itô's formula, stochastic differential delay equation, ultimate boundedness, Probabilities. Mathematical statistics, Analysis, Applied Mathematics
    Subjects:Science > Mathematics > Probabilities. Mathematical statistics
    Department:Faculty of Science > Mathematics and Statistics
    Depositing user: Pure Administrator
    Date deposited:11 Mar 2016 13:27
    Last modified:21 Jan 2020 19:52
    Related URLs:
    URI:https://strathprints.strath.ac.uk/id/eprint/55864
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