Numerical Study of Random Periodic Lipschitz Shadowing of Stochastic Differential Equations
This paper is devoted to a new numerical approach for the possibility of (ω,Lδ)-periodic Lipschitz shadowing of a class of stochastic differential equations. The existence of (ω,Lδ)-periodic Lipschitz shadowing orbits and expression of shadowing distance are established. The numerical implementation...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2018-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2018/1967508 |
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| _version_ | 1841524724561084416 |
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| author | Qingyi Zhan Xiangdong Xie |
| author_facet | Qingyi Zhan Xiangdong Xie |
| author_sort | Qingyi Zhan |
| collection | DOAJ |
| description | This paper is devoted to a new numerical approach for the possibility of (ω,Lδ)-periodic Lipschitz shadowing of a class of stochastic differential equations. The existence of (ω,Lδ)-periodic Lipschitz shadowing orbits and expression of shadowing distance are established. The numerical implementation approaches to the shadowing distance by the random Romberg algorithm are presented, and the convergence of this method is also proved to be mean-square. This ensures the feasibility of the numerical method. The practical use of these theorems and the associated algorithms is demonstrated in the numerical computations of the (ω,Lδ)-periodic Lipschitz shadowing orbits of the stochastic logistic equation. |
| format | Article |
| id | doaj-art-53d3243d719349c6b75abdcdf8677131 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-53d3243d719349c6b75abdcdf86771312025-02-03T05:47:30ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2018-01-01201810.1155/2018/19675081967508Numerical Study of Random Periodic Lipschitz Shadowing of Stochastic Differential EquationsQingyi Zhan0Xiangdong Xie1College of Computer and Information Science, Fujian Agriculture and Forestry University, Fuzhou 350002, ChinaNingde Normal University, Ningde, Fujian 352100, ChinaThis paper is devoted to a new numerical approach for the possibility of (ω,Lδ)-periodic Lipschitz shadowing of a class of stochastic differential equations. The existence of (ω,Lδ)-periodic Lipschitz shadowing orbits and expression of shadowing distance are established. The numerical implementation approaches to the shadowing distance by the random Romberg algorithm are presented, and the convergence of this method is also proved to be mean-square. This ensures the feasibility of the numerical method. The practical use of these theorems and the associated algorithms is demonstrated in the numerical computations of the (ω,Lδ)-periodic Lipschitz shadowing orbits of the stochastic logistic equation.http://dx.doi.org/10.1155/2018/1967508 |
| spellingShingle | Qingyi Zhan Xiangdong Xie Numerical Study of Random Periodic Lipschitz Shadowing of Stochastic Differential Equations Discrete Dynamics in Nature and Society |
| title | Numerical Study of Random Periodic Lipschitz Shadowing of Stochastic Differential Equations |
| title_full | Numerical Study of Random Periodic Lipschitz Shadowing of Stochastic Differential Equations |
| title_fullStr | Numerical Study of Random Periodic Lipschitz Shadowing of Stochastic Differential Equations |
| title_full_unstemmed | Numerical Study of Random Periodic Lipschitz Shadowing of Stochastic Differential Equations |
| title_short | Numerical Study of Random Periodic Lipschitz Shadowing of Stochastic Differential Equations |
| title_sort | numerical study of random periodic lipschitz shadowing of stochastic differential equations |
| url | http://dx.doi.org/10.1155/2018/1967508 |
| work_keys_str_mv | AT qingyizhan numericalstudyofrandomperiodiclipschitzshadowingofstochasticdifferentialequations AT xiangdongxie numericalstudyofrandomperiodiclipschitzshadowingofstochasticdifferentialequations |