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2014 Asymptotic Behaviour and Extinction of Delay Lotka-Volterra Model with Jump-Diffusion
Dan Li, Jing’an Cui, Guohua Song
J. Appl. Math. 2014: 1-16 (2014). DOI: 10.1155/2014/249504


This paper studies the effect of jump-diffusion random environmental perturbations on the asymptotic behaviour and extinction of Lotka-Volterra population dynamics with delays. The contributions of this paper lie in the following: (a) to consider delay stochastic differential equation with jumps, we introduce a proper initial data space, in which the initial data may be discontinuous function with downward jumps; (b) we show that the delay stochastic differential equation with jumps associated with our model has a unique global positive solution and give sufficient conditions that ensure stochastically ultimate boundedness, moment average boundedness in time, and asymptotic polynomial growth of our model; (c) the sufficient conditions for the extinction of the system are obtained, which generalized the former results and showed that the sufficiently large random jump magnitudes and intensity (average rate of jump events arrival) may lead to extinction of the population.


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Dan Li. Jing’an Cui. Guohua Song. "Asymptotic Behaviour and Extinction of Delay Lotka-Volterra Model with Jump-Diffusion." J. Appl. Math. 2014 1 - 16, 2014.


Published: 2014
First available in Project Euclid: 26 March 2014

zbMATH: 07010579
MathSciNet: MR3166757
Digital Object Identifier: 10.1155/2014/249504

Rights: Copyright © 2014 Hindawi

Vol.2014 • 2014
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