Asymptotic Behavior of the Stochastic Rayleigh-van der Pol Equations with Jumps
We study the stability, attractors, and bifurcation of stochastic Rayleigh-van der Pol equations with jumps. We first established the stochastic stability and the large deviations results for the stochastic Rayleigh-van der Pol equations. We then examine the existence limit circle and obtain some ne...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/432704 |
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| _version_ | 1832563927955800064 |
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| author | ZaiTang Huang ChunTao Chen |
| author_facet | ZaiTang Huang ChunTao Chen |
| author_sort | ZaiTang Huang |
| collection | DOAJ |
| description | We study the stability, attractors, and bifurcation of stochastic Rayleigh-van der Pol equations with jumps. We first established the stochastic stability and the large deviations results for the stochastic Rayleigh-van der Pol equations. We then examine the existence limit circle and obtain some new random attractors. We further establish stochastic bifurcation of random attractors. Interestingly, this shows the effect of the Poisson noise which can stabilize or unstabilize the system which is significantly different from the classical Brownian motion process. |
| format | Article |
| id | doaj-art-8690b2a23a774d69b5b468090c1aca9e |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-8690b2a23a774d69b5b468090c1aca9e2025-02-03T01:12:10ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/432704432704Asymptotic Behavior of the Stochastic Rayleigh-van der Pol Equations with JumpsZaiTang Huang0ChunTao Chen1School of Mathematical Sciences, Guangxi Teachers Education University, Nanning 530001, ChinaCollege of Mathematics and Information Science, Guangxi University, Nanning 530004, ChinaWe study the stability, attractors, and bifurcation of stochastic Rayleigh-van der Pol equations with jumps. We first established the stochastic stability and the large deviations results for the stochastic Rayleigh-van der Pol equations. We then examine the existence limit circle and obtain some new random attractors. We further establish stochastic bifurcation of random attractors. Interestingly, this shows the effect of the Poisson noise which can stabilize or unstabilize the system which is significantly different from the classical Brownian motion process.http://dx.doi.org/10.1155/2013/432704 |
| spellingShingle | ZaiTang Huang ChunTao Chen Asymptotic Behavior of the Stochastic Rayleigh-van der Pol Equations with Jumps Abstract and Applied Analysis |
| title | Asymptotic Behavior of the Stochastic Rayleigh-van der Pol Equations with Jumps |
| title_full | Asymptotic Behavior of the Stochastic Rayleigh-van der Pol Equations with Jumps |
| title_fullStr | Asymptotic Behavior of the Stochastic Rayleigh-van der Pol Equations with Jumps |
| title_full_unstemmed | Asymptotic Behavior of the Stochastic Rayleigh-van der Pol Equations with Jumps |
| title_short | Asymptotic Behavior of the Stochastic Rayleigh-van der Pol Equations with Jumps |
| title_sort | asymptotic behavior of the stochastic rayleigh van der pol equations with jumps |
| url | http://dx.doi.org/10.1155/2013/432704 |
| work_keys_str_mv | AT zaitanghuang asymptoticbehaviorofthestochasticrayleighvanderpolequationswithjumps AT chuntaochen asymptoticbehaviorofthestochasticrayleighvanderpolequationswithjumps |