The global analysis is very important for a nonlinear dynamical system which possesses a chaotic saddle and a nonchaotic attractor, especially for the one that is driven by a noise. For a random dynamical system, within which, chaotic saddles exist, it is found that if the noise intensity exceeds a critical value, the so called “noise-induced chaos” is observed. Meanwhile, the exit behavior is also found to be influenced significantly by the existence of chaotic saddles. In the present paper, based on the generalized cell-mapping digraph (GCMD) method, the global dynamical behaviors of a piecewise linear system, wherein a chaotic saddle exists and consists of subharmonic solutions in a wide frequency range, are investigated numerically. Further, in order to simplify the system that is driven by a Gaussian white noise excitation, the stochastic averaging method is applied and through which, a five-dimensional Itô system is obtained. Some of the global dynamical behaviors of the original system are retained in the averaged one and then are analyzed. The researches in this paper show that GCMD method is a good numerical tool to investigate the global behaviors of a nonlinear random dynamical system, and the stochastic averaging method is effective for solving the global problems.
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September 2016
Research-Article
On the Global Analysis of a Piecewise Linear System that is excited by a Gaussian White Noise
Chen Kong,
Chen Kong
State Key Laboratory of Mechanics
and Control of Mechanical Structures,
Nanjing University of Aeronautics
and Astronautics,
Nanjing 210016, China
e-mail: kongchen_bill@126.com
and Control of Mechanical Structures,
Nanjing University of Aeronautics
and Astronautics,
Nanjing 210016, China
e-mail: kongchen_bill@126.com
Search for other works by this author on:
Xue Gao,
Xue Gao
State Key Laboratory of Mechanics
and Control of Mechanical Structures,
Nanjing University of Aeronautics
and Astronautics,
Nanjing 210016, China
e-mail: xgao.detec@nuaa.edu.cn
and Control of Mechanical Structures,
Nanjing University of Aeronautics
and Astronautics,
Nanjing 210016, China
e-mail: xgao.detec@nuaa.edu.cn
Search for other works by this author on:
Xianbin Liu
Xianbin Liu
State Key Laboratory of Mechanics
and Control of Mechanical Structures,
Nanjing University of Aeronautics
and Astronautics,
Nanjing 210016, China
e-mail: xbliu@nuaa.edu.cn
and Control of Mechanical Structures,
Nanjing University of Aeronautics
and Astronautics,
Nanjing 210016, China
e-mail: xbliu@nuaa.edu.cn
Search for other works by this author on:
Chen Kong
State Key Laboratory of Mechanics
and Control of Mechanical Structures,
Nanjing University of Aeronautics
and Astronautics,
Nanjing 210016, China
e-mail: kongchen_bill@126.com
and Control of Mechanical Structures,
Nanjing University of Aeronautics
and Astronautics,
Nanjing 210016, China
e-mail: kongchen_bill@126.com
Xue Gao
State Key Laboratory of Mechanics
and Control of Mechanical Structures,
Nanjing University of Aeronautics
and Astronautics,
Nanjing 210016, China
e-mail: xgao.detec@nuaa.edu.cn
and Control of Mechanical Structures,
Nanjing University of Aeronautics
and Astronautics,
Nanjing 210016, China
e-mail: xgao.detec@nuaa.edu.cn
Xianbin Liu
State Key Laboratory of Mechanics
and Control of Mechanical Structures,
Nanjing University of Aeronautics
and Astronautics,
Nanjing 210016, China
e-mail: xbliu@nuaa.edu.cn
and Control of Mechanical Structures,
Nanjing University of Aeronautics
and Astronautics,
Nanjing 210016, China
e-mail: xbliu@nuaa.edu.cn
1Corresponding author.
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received November 30, 2015; final manuscript received May 18, 2016; published online June 9, 2016. Assoc. Editor: Corina Sandu.
J. Comput. Nonlinear Dynam. Sep 2016, 11(5): 051029 (10 pages)
Published Online: June 9, 2016
Article history
Received:
November 30, 2015
Revised:
May 18, 2016
Citation
Kong, C., Gao, X., and Liu, X. (June 9, 2016). "On the Global Analysis of a Piecewise Linear System that is excited by a Gaussian White Noise." ASME. J. Comput. Nonlinear Dynam. September 2016; 11(5): 051029. https://doi.org/10.1115/1.4033687
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