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Hyperbolic diffusion in chaotic systems

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  • Statistical and Nonlinear Physics
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Abstract

We consider a deterministic process described by a discrete one-dimensional chaotic map and study its diffusive-like properties. Starting with the corresponding Frobenius-Perron equation we derive an approximate evolution equation for the probability distribution which is a partial differential equation of a hyperbolic type. Consequently, the process is correlated, non-Markovian, non-Gaussian and the information propagates with a finite velocity. This is in clear contrast to conventional diffusion processes described by a standard parabolic diffusion equation with an infinite velocity of information propagation. Our approach allows for a more complete characterisation of diffusion dynamics of deterministic systems.

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Authors and Affiliations

  1. Department of Physical Chemistry and Technology of Polymers, Section of Physical Chemistry and Biophysics, Silesian University of Technology, 44-100, Gliwice, Poland

    P. Borys & Z. J. Grzywna

  2. Institute of Physics, University of Silesia, 40-007, Katowice, Poland

    J. Łuczka

Authors
  1. P. Borys
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  2. Z. J. Grzywna
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  3. J. Łuczka
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Correspondence to J. Łuczka.

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Borys, P., Grzywna, Z.J. & Łuczka, J. Hyperbolic diffusion in chaotic systems. Eur. Phys. J. B 83, 223 (2011). https://doi.org/10.1140/epjb/e2011-20162-6

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  • DOI: https://doi.org/10.1140/epjb/e2011-20162-6

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