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Influence of noise on dynamics with fractal Fourier spectra

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  • Zaks, Michael A.

Abstract

In deterministic dynamics, the processes with fractal power spectra occupy the intermediate position between ordered and chaotic temporal behavior. We study numerically the influence of different kinds of noise upon these processes. In general, under the action of noise the spectral measure becomes absolutely continuous and the correlations decay. However, during the certain intermediate period the autocorrelation retains the pattern which is typical for dynamics with fractal spectra. Duration of this period is related to the noise intensity by the power law.

Suggested Citation

  • Zaks, Michael A., 2002. "Influence of noise on dynamics with fractal Fourier spectra," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 310(3), pages 285-307.
    • Handle: RePEc:eee:phsmap:v:310:y:2002:i:3:p:285-307
    DOI: 10.1016/S0378-4371(02)00734-3
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    References listed on IDEAS

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    1. Govindan, R.B. & Vjushin, Dmitry & Brenner, Stephen & Bunde, Armin & Havlin, Shlomo & Schellnhuber, Hans-Joachim, 2001. "Long-range correlations and trends in global climate models: Comparison with real data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 294(1), pages 239-248.
    2. Stanley, H.E. & Buldyrev, S.V. & Goldberger, A.L. & Havlin, S. & Peng, C.-K. & Simons, M., 1993. "Long-range power-law correlations in condensed matter physics and biophysics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 200(1), pages 4-24.
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