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Some exact results on discrete noisy maps

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Zeitschrift für Physik B Condensed Matter

Abstract

Using the Chapman-Kolmogorov type equation introduced by H. Haken and G. Mayer-Kress for discrete time processes we derive forward and backward equations for the corresponding transition probability and obtain an integral equation for the conditional first passage time. In the case of linear dynamics with Gaussian noise we present the exact solution of the Chapman-Kolmogorov equation.

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References

  1. Collet, P., Eckmann, J.P.: Iterated maps on the interval as dynamical system, Birkhauser, Boston, Inc. (1980)

  2. Grossmann, S., Thomae, S.: Z. Naturforsch.32a, 1353 (1977)

    Google Scholar 

  3. Feigenbaum, M.J.: J. Stat. Phys.19, 25 (1978); Phys. Lett.74A, 375 (1979)

    Google Scholar 

  4. Libchaber, A., Maurer, J.: J. Phys. (Paris) Colloq.41, C3–51 (1980)

    Google Scholar 

  5. Giglio, M., Musazzi, S., Perim, U.: Phys. Rev. Lett.47, 243 (1981)

    Google Scholar 

  6. Zippelius, A., Lücke, M.: J. Stat. Phys.24, 345 (1981)

    Google Scholar 

  7. Mayer-Kress, G., Haken, H.: J. Stat. Phys.26, 149 (1981)

    Google Scholar 

  8. Crutchfield, J.P., Huberman, B.A.: Phys. Lett.77A, 407 (1980)

    Google Scholar 

  9. Crutchfield, J.P., Nauenberg, M., Rudnick, J.: Phys. Rev. Lett.46, 935 (1981)

    Google Scholar 

  10. Shraiman, B., Wayne, C.E., Martin, P.C.: Phys. Rev. Lett.46, 933 (1981)

    Google Scholar 

  11. Haken, H., Mayer-Kress, G.: Z. Phys. B-Condensed Matter43, 185 (1981)

    Google Scholar 

  12. Haken, H.: In: Chaos and Order in Nature. Springer Series in Synergetics. Haken, H. (ed.), Vol. 11. Berlin, Heidelberg, New York: Springer Verlag 1981

    Google Scholar 

  13. Stratonovich, R.L.: Topics in the Theory of Random Noise. Vol. 1. New York: Gordon and Breach 1963

    Google Scholar 

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Authors and Affiliations

  1. Institut für Theoretische Physik der Universität, Pfaffenwaldring 57/IV, D-7000, Stuttgart, Federal Republic of Germany

    H. Haken & A. Wunderlin

Authors
  1. H. Haken
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  2. A. Wunderlin
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Haken, H., Wunderlin, A. Some exact results on discrete noisy maps. Z. Physik B - Condensed Matter 46, 181–184 (1982). https://doi.org/10.1007/BF01312723

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  • DOI: https://doi.org/10.1007/BF01312723

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