Stochastic response analysis of noisy system with non-negative real-power restoring force by generalized cell mapping method

doi:10.1007/s10483-015-1918-6

Applied Mathematics and Mechanics (English Edition) ›› 2015, Vol. 36 ›› Issue (3): 329-336.doi: https://doi.org/10.1007/s10483-015-1918-6

Stochastic response analysis of noisy system with non-negative real-power restoring force by generalized cell mapping method

Qun HAN, Wei XU, Xiaole YUE

Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072, China

收稿日期:2014-04-20 修回日期:2014-07-10 出版日期:2015-03-01 发布日期:2015-03-01
通讯作者: Qun HAN E-mail:hanqun@mail.nwpu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Nos. 11172233, 11302169, 11302170, and 11472212) and the Fundamental Research Funds for the Central Universities (No. 3102014JCQ01079)

Stochastic response analysis of noisy system with non-negative real-power restoring force by generalized cell mapping method

Qun HAN, Wei XU, Xiaole YUE

Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072, China

Received:2014-04-20 Revised:2014-07-10 Online:2015-03-01 Published:2015-03-01
Contact: Qun HAN E-mail:hanqun@mail.nwpu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Nos. 11172233, 11302169, 11302170, and 11472212) and the Fundamental Research Funds for the Central Universities (No. 3102014JCQ01079)

摘要/Abstract

摘要： The stochastic response of a noisy system with non-negative real-power restoring force is investigated. The generalized cell mapping (GCM) method is used to compute the transient and stationary probability density functions (PDFs). Combined with the global properties of the noise-free system, the evolutionary process of the transient PDFs is revealed. The results show that stochastic P-bifurcation occurs when the system parameter varies in the response analysis and the stationary PDF evolves from bimodal to unimodal along the unstable manifold during the bifurcation.

关键词: stochastic response, real-power restoring force, bifurcation, generalized cell mapping (GCM) method, probability density function (PDF)

Abstract: The stochastic response of a noisy system with non-negative real-power restoring force is investigated. The generalized cell mapping (GCM) method is used to compute the transient and stationary probability density functions (PDFs). Combined with the global properties of the noise-free system, the evolutionary process of the transient PDFs is revealed. The results show that stochastic P-bifurcation occurs when the system parameter varies in the response analysis and the stationary PDF evolves from bimodal to unimodal along the unstable manifold during the bifurcation.

Key words: generalized cell mapping (GCM) method, probability density function (PDF), bifurcation, stochastic response, real-power restoring force

中图分类号:

O327

Qun HAN;Wei XU;Xiaole YUE. Stochastic response analysis of noisy system with non-negative real-power restoring force by generalized cell mapping method[J]. Applied Mathematics and Mechanics (English Edition), 2015, 36(3): 329-336.

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Stochastic response analysis of noisy system with non-negative real-power restoring force by generalized cell mapping method

Stochastic response analysis of noisy system with non-negative real-power restoring force by generalized cell mapping method

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