This study presents a stochastic approach for the analysis of nonchaotic, chaotic, random and nonchaotic, random and chaotic, and random dynamics of a nonlinear system. The analysis utilizes a Markov process approximation, direct numerical simulations, and a generalized stochastic Melnikov process. The Fokker-Planck equation along with a path integral solution procedure are developed and implemented to illustrate the evolution of probability density functions. Numerical integration is employed to simulate the noise effects on nonlinear responses. In regard to the presence of additive ideal white noise, the generalized stochastic Melnikov process is developed to identify the boundary for noisy chaos. A mathematical representation encompassing all possible dynamical responses is provided. Numerical results indicate that noisy chaos is a possible intermediate state between deterministic and random dynamics. A global picture of the system behavior is demonstrated via the transition of probability density function over its entire evolution. It is observed that the presence of external noise has significant effects over the transition between different response states and between co-existing attractors.
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June 1996
Technical Papers
Analysis of a Nonlinear System Exhibiting Chaotic, Noisy Chaotic, and Random Behaviors
H. Lin,
H. Lin
Department of Civil Engineering, Oregon State University, Corvallis, OR 97331-2303
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S. C. S. Yim
S. C. S. Yim
Department of Civil Engineering, Oregon State University, Corvallis, OR 97331-2303
Search for other works by this author on:
H. Lin
Department of Civil Engineering, Oregon State University, Corvallis, OR 97331-2303
S. C. S. Yim
Department of Civil Engineering, Oregon State University, Corvallis, OR 97331-2303
J. Appl. Mech. Jun 1996, 63(2): 509-516 (8 pages)
Published Online: June 1, 1996
Article history
Received:
March 31, 1994
Revised:
May 18, 1995
Online:
October 26, 2007
Citation
Lin, H., and Yim, S. C. S. (June 1, 1996). "Analysis of a Nonlinear System Exhibiting Chaotic, Noisy Chaotic, and Random Behaviors." ASME. J. Appl. Mech. June 1996; 63(2): 509–516. https://doi.org/10.1115/1.2788897
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