Asymptotic Behaviour and Extinction of Delay Lotka-Volterra Model with Jump-Diffusion
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...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
|
| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/249504 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850162165539930112 |
|---|---|
| author | Dan Li Jing’an Cui Guohua Song |
| author_facet | Dan Li Jing’an Cui Guohua Song |
| author_sort | Dan Li |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-fd08fc2fccf34346973cd6d12f1fd2e7 |
| institution | OA Journals |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-fd08fc2fccf34346973cd6d12f1fd2e72025-08-20T02:22:38ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/249504249504Asymptotic Behaviour and Extinction of Delay Lotka-Volterra Model with Jump-DiffusionDan Li0Jing’an Cui1Guohua Song2Foundation Department, Hohai University Wentian College, Maanshan, Anhui 243000, ChinaSchool of Science, Beijing University of Civil Engineering and Architecture, Beijing 100044, ChinaSchool of Science, Beijing University of Civil Engineering and Architecture, Beijing 100044, ChinaThis 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.http://dx.doi.org/10.1155/2014/249504 |
| spellingShingle | Dan Li Jing’an Cui Guohua Song Asymptotic Behaviour and Extinction of Delay Lotka-Volterra Model with Jump-Diffusion Journal of Applied Mathematics |
| title | Asymptotic Behaviour and Extinction of Delay Lotka-Volterra Model with Jump-Diffusion |
| title_full | Asymptotic Behaviour and Extinction of Delay Lotka-Volterra Model with Jump-Diffusion |
| title_fullStr | Asymptotic Behaviour and Extinction of Delay Lotka-Volterra Model with Jump-Diffusion |
| title_full_unstemmed | Asymptotic Behaviour and Extinction of Delay Lotka-Volterra Model with Jump-Diffusion |
| title_short | Asymptotic Behaviour and Extinction of Delay Lotka-Volterra Model with Jump-Diffusion |
| title_sort | asymptotic behaviour and extinction of delay lotka volterra model with jump diffusion |
| url | http://dx.doi.org/10.1155/2014/249504 |
| work_keys_str_mv | AT danli asymptoticbehaviourandextinctionofdelaylotkavolterramodelwithjumpdiffusion AT jingancui asymptoticbehaviourandextinctionofdelaylotkavolterramodelwithjumpdiffusion AT guohuasong asymptoticbehaviourandextinctionofdelaylotkavolterramodelwithjumpdiffusion |