Journal article 1176 views 244 downloads
Impacts of noise on ordinary differential equations
Guangying Lv,
Jinqiao Duan,
Liang Wang,
Jiang-lun Wu 
Dynamic Systems and Applications, Volume: 27, Issue: 2, Pages: 25 - 36
Swansea University Author:
Jiang-lun Wu
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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...
| Published in: | Dynamic Systems and Applications |
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| ISBN: | ISSN 1056-2176 |
| Published: |
USA
Dynamic Publishers
2018
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa35933 |
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| 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 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. |
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| Keywords: |
t\^{o}'s formula; singularities; Stochastic differential equation; Impact of noise. |
| College: |
Faculty of Science and Engineering |
| Issue: |
2 |
| Start Page: |
25 |
| End Page: |
36 |