中国物理B ›› 2005, Vol. 14 ›› Issue (9): 1691-1697.doi: 10.1088/1009-1963/14/9/002

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A method of moments for calculating dynamic responses beyond linear response theory

康艳梅1, 徐健学2, 谢勇2   

  1. (1)Institute of Information & System Science, School of Science,Xi'an Jiaotong University, Xi'an 710049, China；Institute of Nonlinear Dynamics, School of Architectural Engineering & Mechanics, Xi'an Jiaotong University, Xi'an 710049, China; (2)Institute of Nonlinear Dynamics, School of Architectural Engineering & Mechanics,Xi'an Jiaotong University, Xi'an 710049, China
  • 收稿日期:2005-03-18 修回日期:2005-05-28 出版日期:2005-09-20 发布日期:2005-09-20
  • 基金资助:
    Project supported by BH foundation of XJTU and the major program of the National Natural Science Foundation of China (Grant No 10432010).

A method of moments for calculating dynamic responses beyond linear response theory

Kang Yan-Mei (康艳梅)ab, Xu Jian-Xue (徐健学)b, Xie Yong (谢勇)b   

  1. a Institute of Information & System Science, School of Science,Xi'an Jiaotong University, Xi'an 710049, Chinab Institute of Nonlinear Dynamics, School of Architectural Engineering & Mechanics, Xi'an Jiaotong University, Xi'an 710049, China
  • Received:2005-03-18 Revised:2005-05-28 Online:2005-09-20 Published:2005-09-20
  • Supported by:
    Project supported by BH foundation of XJTU and the major program of the National Natural Science Foundation of China (Grant No 10432010).

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摘要： A method of moments for calculating the dynamic response of periodically driven overdamped nonlinear stochastic systems in the general response sense is proposed, which is a modification of the method of moments confined within linear response theory. The calculating experience suggests that the proposed technique is simple and efficient in implementation, and the comparison with stochastic simulation shows that the first three orders of susceptibilities calculated by the proposed technique have high accuracy. The dependence of the spectral amplification parameters at the first three harmonics on the noise intensity is also investigated, and another observed phenomenon of stochastic resonance in the systems induced by the location of a single periodic orbit is disclosed and explained.

关键词: a method of moments, dynamic susceptibility, spectral amplification factor, stochastic resonance

Abstract: A method of moments for calculating the dynamic response of periodically driven overdamped nonlinear stochastic systems in the general response sense is proposed, which is a modification of the method of moments confined within linear response theory. The calculating experience suggests that the proposed technique is simple and efficient in implementation, and the comparison with stochastic simulation shows that the first three orders of susceptibilities calculated by the proposed technique have high accuracy. The dependence of the spectral amplification parameters at the first three harmonics on the noise intensity is also investigated, and another observed phenomenon of stochastic resonance in the systems induced by the location of a single periodic orbit is disclosed and explained.

Key words: a method of moments, dynamic susceptibility, spectral amplification factor, stochastic resonance

中图分类号:  (Numerical approximation and analysis)

  • 02.60.-x
02.50.Ey (Stochastic processes) 05.40.-a (Fluctuation phenomena, random processes, noise, and Brownian motion) 02.30.Hq (Ordinary differential equations)