Hopf Bifurcations of a Stochastic Fractional-Order Van der Pol System
The Hopf bifurcation of a fractional-order Van der Pol (VDP for short) system with a random parameter is investigated. Firstly, the Chebyshev polynomial approximation is applied to study the stochastic fractional-order system. Based on the method, the stochastic system is reduced to the equivalent d...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/835482 |
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| _version_ | 1832555837763092480 |
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| author | Xiaojun Liu Ling Hong Lixin Yang |
| author_facet | Xiaojun Liu Ling Hong Lixin Yang |
| author_sort | Xiaojun Liu |
| collection | DOAJ |
| description | The Hopf bifurcation of a fractional-order Van der Pol (VDP for short) system with a random parameter is investigated. Firstly, the Chebyshev polynomial approximation is applied to study the stochastic fractional-order system. Based on the method, the stochastic system is reduced to the equivalent deterministic one, and then the responses of the stochastic system can be obtained by numerical methods. Then, according to the existence conditions of Hopf bifurcation, the critical parameter value of the bifurcation is obtained by theoretical analysis. Then, numerical simulations are carried out to verify the theoretical results. |
| format | Article |
| id | doaj-art-04ae8ce12b0c4a34b1e55f0df4e5a697 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-04ae8ce12b0c4a34b1e55f0df4e5a6972025-02-03T05:46:58ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/835482835482Hopf Bifurcations of a Stochastic Fractional-Order Van der Pol SystemXiaojun Liu0Ling Hong1Lixin Yang2State Key Laboratory for Strength and Vibration of Mechanical Structures, Xi’an Jiaotong University, Xi’an 710049, ChinaState Key Laboratory for Strength and Vibration of Mechanical Structures, Xi’an Jiaotong University, Xi’an 710049, ChinaState Key Laboratory for Strength and Vibration of Mechanical Structures, Xi’an Jiaotong University, Xi’an 710049, ChinaThe Hopf bifurcation of a fractional-order Van der Pol (VDP for short) system with a random parameter is investigated. Firstly, the Chebyshev polynomial approximation is applied to study the stochastic fractional-order system. Based on the method, the stochastic system is reduced to the equivalent deterministic one, and then the responses of the stochastic system can be obtained by numerical methods. Then, according to the existence conditions of Hopf bifurcation, the critical parameter value of the bifurcation is obtained by theoretical analysis. Then, numerical simulations are carried out to verify the theoretical results.http://dx.doi.org/10.1155/2014/835482 |
| spellingShingle | Xiaojun Liu Ling Hong Lixin Yang Hopf Bifurcations of a Stochastic Fractional-Order Van der Pol System Abstract and Applied Analysis |
| title | Hopf Bifurcations of a Stochastic Fractional-Order Van der Pol System |
| title_full | Hopf Bifurcations of a Stochastic Fractional-Order Van der Pol System |
| title_fullStr | Hopf Bifurcations of a Stochastic Fractional-Order Van der Pol System |
| title_full_unstemmed | Hopf Bifurcations of a Stochastic Fractional-Order Van der Pol System |
| title_short | Hopf Bifurcations of a Stochastic Fractional-Order Van der Pol System |
| title_sort | hopf bifurcations of a stochastic fractional order van der pol system |
| url | http://dx.doi.org/10.1155/2014/835482 |
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