Noise-induced instability

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Abstract
We have found that the regular motion of an integrable system becomes erratic when a weak white noise is added. The interaction between dynamic and stochastic forces gives rise to an erratic power spectrum, positive Lyapunov exponents, and nonzero correlation exponent independent of embedding dimensions. Since the weak noise drives the systems to unstable fixed points that the dynamic force cannot reach, we call the onset of this erratic behavior the noise-induced instability. The results also indicate that the nonzero correlation exponents independent of embedding dimensions are not necessarily related to the deterministic chaos and that caution should be used in applying this technique to distinguish chaos from noise.