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Random pining of localized states and the birth of deterministic disorder within gradient models

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Abstract

The birth of spatial disorder from almost regular initial conditions within the Swift-Hohenberg model equation with subcritical bifurcation is considered. The complexity of the space series (measured by the spatialK 2-entropy) grows with time and reaches a stationary value depending on the period of the initial regular disturbance. A qualitative model is suggested describing the process via the birth of localized structures and its subsequent disordering due to weak interaction.

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References

  1. V. S. Afraimovich, A. B. Ezersky, M. I. Rabinovich, M. A. Shereshevsky, and A. L. Zheleznyak, Dynamical description of spatial disorder,Physica D 58:331 (1992).

    Google Scholar 

  2. P. Coullet, J. Lega, B. Houchmanzadeh, and J. Lajzerowicz, Breaking chirality in nonequilibrium systems.Phys. Rev. Lett. 65:1352 (1990).

    Google Scholar 

  3. P. Coullet, C. Elphick, and D. Repaux, Nature of spatial chaos,Phys. Rev. Lett. 58:431 (1987).

    Google Scholar 

  4. P. Grassberger and I. Procaccia, Characterization of strange attractors.Phys. Rev. Lett. 50:346 (1983).

    Google Scholar 

  5. A. M. Fraser and H. L. Swinney, Independent coordinates for strange attractors from mutual information,Phys. Rev. A 33:1134 (1986).

    Google Scholar 

  6. K. A. Gorshkov and L. A. Ostrovsky, Interactions of solitons in nonintegrable systems: Direct perturbation method and applications,Physica D 3:428 (1981).

    Google Scholar 

  7. V. S. Afraimovich, On the Lyapunov dimension of invariant sets in a model of an active medium,Selecta Math. Sovet. 10:91 (1991).

    Google Scholar 

  8. J. M. Ziman,Models of Disorder (Cambridge University Press, Cambridge, 1979).

    Google Scholar 

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Author notes

  1. L. S. Tsimring

    Present address: Institute for Nonlinear Science, University of California at San Diego, 92093-0402, La Jolla, California

Authors and Affiliations

  1. Institute of Applied Physics, Russian Academy of Science, 603600, Nizhni Novgorod, Russia

    K. A. Gorshkov, L. N. Korzinov, M. I. Rabinovich & L. S. Tsimring

Authors
  1. K. A. Gorshkov
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  2. L. N. Korzinov
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  3. M. I. Rabinovich
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  4. L. S. Tsimring
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Gorshkov, K.A., Korzinov, L.N., Rabinovich, M.I. et al. Random pining of localized states and the birth of deterministic disorder within gradient models. J Stat Phys 74, 1033–1045 (1994). https://doi.org/10.1007/BF02188216

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  • DOI: https://doi.org/10.1007/BF02188216

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