Asymptotic Behaviour and Extinction of Delay Lotka‐Volterra Model with Jump‐Diffusion

Dan Li, Jing’an Cui and Guohua Song

Journal of Applied Mathematics, 2014, vol. 2014, issue 1

Abstract: 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.

Date: 2014
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1155/2014/249504

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2014:y:2014:i:1:n:249504

Access Statistics for this article

More articles in Journal of Applied Mathematics from John Wiley & Sons
Bibliographic data for series maintained by Wiley Content Delivery ().