Stochastic response of fractional-order van der Pol oscillator
We studied the response of fractional-order van de Pol oscillator to Gaussian white noise excitation in this letter. An equivalent integral-order nonlinear stochastic system is obtained to replace the given system based on the principle of minimum mean-square error. Through stochastic averaging, an...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Elsevier
2014-01-01
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| Series: | Theoretical and Applied Mechanics Letters |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2095034915302920 |
| _version_ | 1819081636746100736 |
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| author | Lincong Chen Weiqiu Zhu |
| author_facet | Lincong Chen Weiqiu Zhu |
| author_sort | Lincong Chen |
| collection | DOAJ |
| description | We studied the response of fractional-order van de Pol oscillator to Gaussian white noise excitation in this letter. An equivalent integral-order nonlinear stochastic system is obtained to replace the given system based on the principle of minimum mean-square error. Through stochastic averaging, an averaged Itô equation is deduced. We obtained the Fokker-Planck-Kolmogorov equation connected to the averaged Itô equation and solved it to yield the approximate stationary response of the system. The analytical solution is confirmed by using Monte Carlo simulation. |
| first_indexed | 2024-12-21T20:03:56Z |
| format | Article |
| id | doaj.art-d03f8bac1ba240ce80c4992d7c17d074 |
| institution | Directory Open Access Journal |
| issn | 2095-0349 |
| language | English |
| last_indexed | 2024-12-21T20:03:56Z |
| publishDate | 2014-01-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Theoretical and Applied Mechanics Letters |
| spelling | doaj.art-d03f8bac1ba240ce80c4992d7c17d0742022-12-21T18:51:54ZengElsevierTheoretical and Applied Mechanics Letters2095-03492014-01-014110.1063/2.1401310Stochastic response of fractional-order van der Pol oscillatorLincong Chen0Weiqiu Zhu1College of Civil Engineering, Huaqiao University, Xiamen 361021, ChinaDepartment of Mechanics, Zhejiang University, Hangzhou 310027, ChinaWe studied the response of fractional-order van de Pol oscillator to Gaussian white noise excitation in this letter. An equivalent integral-order nonlinear stochastic system is obtained to replace the given system based on the principle of minimum mean-square error. Through stochastic averaging, an averaged Itô equation is deduced. We obtained the Fokker-Planck-Kolmogorov equation connected to the averaged Itô equation and solved it to yield the approximate stationary response of the system. The analytical solution is confirmed by using Monte Carlo simulation.http://www.sciencedirect.com/science/article/pii/S2095034915302920fractional-order van de Pol oscillatorGaussian white noisestationary responseequivalent nonlinear system methodstochastic averaging |
| spellingShingle | Lincong Chen Weiqiu Zhu Stochastic response of fractional-order van der Pol oscillator Theoretical and Applied Mechanics Letters fractional-order van de Pol oscillator Gaussian white noise stationary response equivalent nonlinear system method stochastic averaging |
| title | Stochastic response of fractional-order van der Pol oscillator |
| title_full | Stochastic response of fractional-order van der Pol oscillator |
| title_fullStr | Stochastic response of fractional-order van der Pol oscillator |
| title_full_unstemmed | Stochastic response of fractional-order van der Pol oscillator |
| title_short | Stochastic response of fractional-order van der Pol oscillator |
| title_sort | stochastic response of fractional order van der pol oscillator |
| topic | fractional-order van de Pol oscillator Gaussian white noise stationary response equivalent nonlinear system method stochastic averaging |
| url | http://www.sciencedirect.com/science/article/pii/S2095034915302920 |
| work_keys_str_mv | AT lincongchen stochasticresponseoffractionalordervanderpoloscillator AT weiqiuzhu stochasticresponseoffractionalordervanderpoloscillator |