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A Variable Delay Lotka-Volterra Population Model with White Noise

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Author:
No author available
Journal Title:
JOURNAL OF BIOMATHEMATICS
Issue:
2
DOI:
No doi available
Key Word:
随机 Loltka-Volterr模型;可变时滞;一致有界性;It(o)公式;Stochastic Lotka-Volterra Model;Variable Delay;Ultimate Boundedness;It(o)'s formula

Abstract: Since population models are often subject to environmental noise, in this paper we stochastically perturb the Lotka-Volterra model with variable delay x(t)=diag(x(t))[b + Ax(t) + Bx(t-δ(t))] into the Ito form dx(t) = diag(x(t))[(b+ Ax(t) + Bx(t-δ(t)))dt+(Qx(t) + Rx(t -δ(t))dw(t)]. We reveal that the environmental noise will not only suppress a potential population explosion in such model but will also make the solutions to be stochastically ultimately bounded without any additional condition on the coefficients b, A, B.

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