Interaction Between Chaos and Noise in Mechanical Vibration Systems

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We investigate experimental nonchaotic behavior by using probability density functions of local expansion rates of Poincare maps of observed data. The obtained results clearly showed that in some cases the experimental nonchaotic behavior resembles deterministic chaos in properties such as expanding and folding process of attractors and well modeled by the stochastic model rather than the deterministic model. We first numerically examine bifurcations of signs of largest Liapunov exponents of stochastic systems to confirm nearly zero valued largest Liapunov exponents observed in the experiments. We then numerically and experimentally investigate the chaotic and nonchaotic behaviors. Information dimension and spectral distribution function are used to characterize similarities and differences among the deterministic, stochastic, and experimental behaviors.The following results are obtained :In the chaotic region far from the neutral stable point, fractal and spectral characteristics of the experimental behavior is well reproduced by both the deterministic model and the stochastic model.In the nonchaotic region near the neutral stable point, fractal characteristics of the experimental behavior can be reproduced only by the stochastic model. Conversely, in some cases, spectral characteristics of the experimental behavior can be reproduced by both the deterministic model and the stochastic model.The above results lead to the conclusion that experimental nonchaotic behavior we observed is well modeled by stochastic nonchaotic behavior near neutral stable points and characterized as being different in fractal characteristics and similar in spectral characteristics to the deterministic chaos.