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Applicable Analysis
An International Journal
Volume 88, 2009 - Issue 9
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Original Articles

Stochastic delay population systems

Pages 1303-1320 | Received 28 Jan 2009, Accepted 20 Aug 2009, Published online: 03 Nov 2009
 

Abstract

In this article we stochastically perturb the classical non-autonomous delay Lotka–Volterra model

into the stochastic delay population system (SDPS)
Different from most of the existing papers [A. Bahar and X. Mao, Stochastic delay Lotka–Volterra model, J. Math. Anal. Appl. 292 (2004), 364–380, A. Bahar and X. Mao, Stochastic delay population dynamics, J. Pure Appl. Math. 11 (2004), 377–400, X. Mao, Delay population dynamics and environmental noise, Stochastics Dyn. 5(2) (2005), pp. 149–162], the system parameters in this article are time-dependent. We will give a sufficient condition under which the SDPS will have a unique global positive solution. We will then establish some new asymptotic properties for the moments of the solution. In particular, we will discuss two fundamental problems in population systems, namely ultimate boundedness and extinction.

AMS Subject Classifications:

Acknowledgement

The author would like to thank the referees for their helpful comments.

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