| Stochastic period-doubling bifurcation in biharmonic driven Dulling system with random parameter |
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| 作者姓名： | 徐伟 马少娟 谢文贤 |
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| 作者单位： | Department of Applied Mathematics, Northwestern
Polytechnical University, Xi'an 710072, China;Department of Applied Mathematics, Northwestern
Polytechnical University, Xi'an 710072, China;Department of Applied Mathematics, Northwestern
Polytechnical University, Xi'an 710072, China |
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| 基金项目： | Project supported by the National
Natural Science Foundation of China (Grant Nos 10472091 and
10332030). |
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| 摘 要： | Stochastic period-doubling bifurcation is explored in a forced Duffing system with a bounded random parameter as an additional weak harmonic perturbation added to the system. Firstly, the biharmonic driven Duffing system with a random parameter is reduced to its equivalent deterministic one, and then the responses of the stochastic system can be obtained by available effective numerical methods. Finally, numerical simulations show that the phase of the additional weak harmonic perturbation has great influence on the stochastic period-doubling bifurcation in the biharmonic driven Duffing system. It is emphasized that, different from the deterministic biharmonic driven Duffing system, the intensity of random parameter in the Duffing system can also be taken as a bifurcation parameter, which can lead to the stochastic period-doubling bifurcations.
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| 关 键 词： | 随机参数 随机双周期交叉 正交多项近似值 数学算法 |
| 收稿时间： | 2007-04-12 |
| 修稿时间： | 9/9/2007 12:00:00 AM |
Stochastic period-doubling bifurcation in biharmonic driven Duffing system with random parameter |
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| Xu Wei,Ma Shao-Juan and Xie Wen-Xian.Stochastic period-doubling bifurcation in biharmonic driven Dulling system with random parameter[J].Chinese Physics B,2008,17(3):857-864. |
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| Authors: | Xu Wei Ma Shao-Juan and Xie Wen-Xian |
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| Institution: | Department of Applied Mathematics, Northwestern
Polytechnical University, Xi'an 710072, China |
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| Abstract: | Stochastic period-doubling bifurcation is explored in a forced Duffing system with a bounded random parameter as an additional weak harmonic perturbation added to the system. Firstly, the biharmonic driven Duffing system with a random parameter is reduced to its equivalent deterministic one, and then the responses of the stochastic system can be obtained by available effective numerical methods. Finally, numerical simulations show that the phase of the additional weak harmonic perturbation has great influence on the stochastic period-doubling bifurcation in the biharmonic driven Duffing system. It is emphasized that, different from the deterministic biharmonic driven Duffing system, the intensity of random parameter in the Duffing system can also be taken as a bifurcation parameter, which can lead to the stochastic period-doubling bifurcations. |
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| Keywords: | random parameter stochastic
Duffing system stochastic period-doubling bifurcation orthogonal
polynomial approximation |
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