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Impacts of noise on ordinary differential equations

Guangying Lv, Jinqiao Duan, Liang Wang, Jiang-lun Wu Orcid Logo

Dynamic Systems and Applications, Volume: 27, Issue: 2, Pages: 25 - 36

Swansea University Author: Jiang-lun Wu Orcid Logo

DOI (Published version): 10.12732/dsa.v27i2.2

Abstract

In this paper, we consider the impacts of noise on ordinary differential equations. We first prove that the weak noise can change the value of equilibrium and the strong noise can destroy the stability of equilibrium.Then we consider the competition between the nonlinear term and noise term, which s...

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Published in: Dynamic Systems and Applications
ISBN: ISSN 1056-2176
Published: USA Dynamic Publishers 2018
URI: https://cronfa.swan.ac.uk/Record/cronfa35933
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first_indexed 2017-10-04T19:52:36Z
last_indexed 2018-04-02T13:31:49Z
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spelling 2018-04-02T11:58:11.6576400 v2 35933 2017-10-04 Impacts of noise on ordinary differential equations dbd67e30d59b0f32592b15b5705af885 0000-0003-4568-7013 Jiang-lun Wu Jiang-lun Wu true false 2017-10-04 SMA In this paper, we consider the impacts of noise on ordinary differential equations. We first prove that the weak noise can change the value of equilibrium and the strong noise can destroy the stability of equilibrium.Then we consider the competition between the nonlinear term and noise term, which shows that noise can induce singularities (finite time blow up of solutions) and that the nonlinear term can prevent the singularities. Besides that, some simulations are given in order to illustrate our results. Journal Article Dynamic Systems and Applications 27 2 25 36 Dynamic Publishers USA ISSN 1056-2176 t\^{o}&apos;s formula; singularities; Stochastic differential equation; Impact of noise. 3 3 2018 2018-03-03 10.12732/dsa.v27i2.2 COLLEGE NANME Mathematics COLLEGE CODE SMA Swansea University 2018-04-02T11:58:11.6576400 2017-10-04T17:30:17.8528054 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Guangying Lv 1 Jinqiao Duan 2 Liang Wang 3 Jiang-lun Wu 0000-0003-4568-7013 4 0035933-05032018115646.pdf LvDuanWangWu_DynamicSystemsandApplications2018.pdf 2018-03-05T11:56:46.8630000 Output 1670704 application/pdf Corrected Version of Record true 2018-03-05T00:00:00.0000000 false eng
title Impacts of noise on ordinary differential equations
spellingShingle Impacts of noise on ordinary differential equations
Jiang-lun Wu
title_short Impacts of noise on ordinary differential equations
title_full Impacts of noise on ordinary differential equations
title_fullStr Impacts of noise on ordinary differential equations
title_full_unstemmed Impacts of noise on ordinary differential equations
title_sort Impacts of noise on ordinary differential equations
author_id_str_mv dbd67e30d59b0f32592b15b5705af885
author_id_fullname_str_mv dbd67e30d59b0f32592b15b5705af885_***_Jiang-lun Wu
author Jiang-lun Wu
author2 Guangying Lv
Jinqiao Duan
Liang Wang
Jiang-lun Wu
format Journal article
container_title Dynamic Systems and Applications
container_volume 27
container_issue 2
container_start_page 25
publishDate 2018
institution Swansea University
isbn ISSN 1056-2176
doi_str_mv 10.12732/dsa.v27i2.2
publisher Dynamic Publishers
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics
document_store_str 1
active_str 0
description In this paper, we consider the impacts of noise on ordinary differential equations. We first prove that the weak noise can change the value of equilibrium and the strong noise can destroy the stability of equilibrium.Then we consider the competition between the nonlinear term and noise term, which shows that noise can induce singularities (finite time blow up of solutions) and that the nonlinear term can prevent the singularities. Besides that, some simulations are given in order to illustrate our results.
published_date 2018-03-03T03:44:51Z
_version_ 1763752114279940096
score 11.013148

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