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Analogy between the Lorenz strange attractor and a bistable stochastic oscillator

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Abstract

The relation between the aperiodic solution of the Lorenz model and that of a stochastic anharmonic oscillator is explored. The stochastic oscillator is constructed by replacing ż(t) in the Lorenz model by a stochastic variableζ(t) of specified statistics. The resulting system is of course not isomorphic to the Lorenz model, but does share with it a number of statistical properties. Thus, within the confines of these measures the two systems are physically very similar.

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References

  1. G. Ahlers and R. W. Walden,Phys. Rev. Lett. 44:445 (1980).

    Google Scholar 

  2. E. N. Lorenz,J. Atmos. Sci. 20:130 (1963).

    Google Scholar 

  3. H. Haken,Phys. Lett. 53A:77 (1975).

    Google Scholar 

  4. D. S. Ray,Phys. Rev. A 29:3440 (1984).

    Google Scholar 

  5. S. A. Orszag, inProceedings of the 1973 Les Houche Summer School of Theoretical Physics.

  6. M. Lücke,J. Stat. Phys. 15:455 (1976).

    Google Scholar 

  7. Z. Zippelius and M. Lücke,J. Stat. Phys. 24:345 (1981).

    Google Scholar 

  8. Y. Aizawa,Prog. Theor. Phys. 68:64 (1982).

    Google Scholar 

  9. E. Knobloch,J. Stat. Phys. 20:695 (1979).

    Google Scholar 

  10. P. Holmes and D. Rand,Int. J. Non-Linear Mech. 15:449 (1980).

    Google Scholar 

  11. K. A. Wiesenfeld and E. Knobloch,Phys. Rev. A 26:2946 (1982).

    Google Scholar 

  12. V. Seshadri, B. J. West, and K. Lindenberg,Physica 107A:219 (1981).

    Google Scholar 

  13. B. Saltzman,J. Atmos. Sci. 19:329 (1962).

    Google Scholar 

  14. D. Ruelle and F. Takens,Commun. Math. Phys. 20:167 (1971).

    Google Scholar 

  15. K. Takeyama,Prog. Theor. Phys. 63:91 (1980).

    Google Scholar 

  16. K. Lindenberg, K. E. Shuler, V. Seshadri, and B. J. West, inProbabilistic Analysis and Related Topics, Vol.3, A. T. Bharucha-Reid, ed. (Academic Press, New York, 1983).

    Google Scholar 

  17. R. L. Stratonovich,Topics in the Theory of Random Noise, Vol. 1 (Gordon and Breach, New York, 1976).

    Google Scholar 

  18. V. Seshadri, B. J. West, and K. Lindenberg,J. Sound Vib. 68:553 (1980).

    Google Scholar 

  19. Z. Schuss,Theory and Applications of Stochastic Differential Equations (Wiley, New York, 1980).

    Google Scholar 

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Authors and Affiliations

  1. Department of Chemistry, University of California-San Diego, 92093, La Jolla, California

    J. Kottalam & Katja Lindenberg

  2. Division of Applied Nonlinear Problems, La Jolla Institute, 92038, La Jolla, California

    Bruce J. West

Authors
  1. J. Kottalam
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  2. Bruce J. West
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  3. Katja Lindenberg
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Kottalam, J., West, B.J. & Lindenberg, K. Analogy between the Lorenz strange attractor and a bistable stochastic oscillator. J Stat Phys 46, 119–133 (1987). https://doi.org/10.1007/BF01010335

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  • DOI: https://doi.org/10.1007/BF01010335

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