Stochastic sensitivity analysis of non-autonomous nonlinear dynamical systems driven by Gaussian white noise
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- 英文论文题名：Stochastic sensitivity analysis of non-autonomous nonlinear dynamical systems driven by Gaussian white noise
- 论文作者：孙亚辉 ; 洪灵 ; 江俊 ; 李自刚
- 英文论文作者：SUN Ya-hui ; HONG Ling ; JIANG Jun ; LI Zi-gang ; State Key Laboratory for Strength and Vibration ; Xi’an Jiaotong University
- 年：2016
- 作者机构：State Key Laboratory for Strength and Vibration, Xi’an Jiaotong University;
- 英文论文关键词：Stochastic sensitivity analysis ; non-autonomous nonlinear dynamical systems ; stroboscopic map ; mapping systems
- 会议召开时间：2016-05-06
- 会议录名称：第十届动力学与控制学术会议摘要集
- 语种：英文
- 分类号：O19
- 学会代码：AGLU
- 会议名称：第十届动力学与控制学术会议
- 会议地点：中国四川成都
- 主办单位：中国力学学会动力学与控制专业委员会
- 学会名称：中国力学学会
- 页数：1
- 文件大小：739k
- 原文格式：D
- 会议级别：全国
摘要
The stochastic sensitivity of the non-autonomous nonlinear dynamical system subject to Gaussian white noise is analyzed in this paper. At first, the period-T attractor of a nonautonomous nonlinear dynamical system is discretized into the period-N cycle of a mapping system based on the stroboscopic map. A method with high accuracy is adopted in this paper to approximate the stroboscopic map and thus expend the range of its application. Then, stochastic sensitivity functions of the period-N cycle are calculated, and after that the stochastic sensitivity of the non-autonomous nonlinear dynamical system are analyzed. In this paper, the forced Duffing-Van der Pol oscillator which has a period-1 attractor and the forced Rayleigh-Duffing oscillator which has a period-3 attractor are given to demonstrate the validity of the method. The results show that the trends of the stochastic attractor and the confidence ellipses are consistent and the evolution of the maximum eigenvalue of stochastic sensitivity function within one period illustrates the sensitivity of the stochastic attractor.
The stochastic sensitivity of the non-autonomous nonlinear dynamical system subject to Gaussian white noise is analyzed in this paper. At first, the period-T attractor of a nonautonomous nonlinear dynamical system is discretized into the period-N cycle of a mapping system based on the stroboscopic map. A method with high accuracy is adopted in this paper to approximate the stroboscopic map and thus expend the range of its application. Then, stochastic sensitivity functions of the period-N cycle are calculated, and after that the stochastic sensitivity of the non-autonomous nonlinear dynamical system are analyzed. In this paper, the forced Duffing-Van der Pol oscillator which has a period-1 attractor and the forced Rayleigh-Duffing oscillator which has a period-3 attractor are given to demonstrate the validity of the method. The results show that the trends of the stochastic attractor and the confidence ellipses are consistent and the evolution of the maximum eigenvalue of stochastic sensitivity function within one period illustrates the sensitivity of the stochastic attractor.
The stochastic sensitivity of the non-autonomous nonlinear dynamical system subject to Gaussian white noise is analyzed in this paper. At first, the period-T attractor of a nonautonomous nonlinear dynamical system is discretized into the period-N cycle of a mapping system based on the stroboscopic map. A method with high accuracy is adopted in this paper to approximate the stroboscopic map and thus expend the range of its application. Then, stochastic sensitivity functions of the period-N cycle are calculated, and after that the stochastic sensitivity of the non-autonomous nonlinear dynamical system are analyzed. In this paper, the forced Duffing-Van der Pol oscillator which has a period-1 attractor and the forced Rayleigh-Duffing oscillator which has a period-3 attractor are given to demonstrate the validity of the method. The results show that the trends of the stochastic attractor and the confidence ellipses are consistent and the evolution of the maximum eigenvalue of stochastic sensitivity function within one period illustrates the sensitivity of the stochastic attractor.
引文