Asymptotic behaviour and extinction of delay Lotka-Volterra model with jump-diffusion
type: Item
instance of: scholarly article
title: Asymptotic behaviour and extinction of delay Lotka-Volterra model with jump-diffusion
zbMATH Open document ID: 1406.60088
DOI: 10.1155/2014/249504
author: Dan Li
author: Guohua Song
author: Jing-An Cui
published in: Journal of Applied Mathematics
publication date: 2019-02-01T00:00:00Z
review text: Summary: 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.
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 34F05
Mathematics Subject Classification ID: 60J75
zbMATH DE Number: 7010579
Wikidata QID: Q59050498
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/249504
OpenAlex ID: W2094231522
DBLP publication ID: journals/jam/LiCG14
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description: scientific article; zbMATH DE number 7010579