https://doi.org/10.1140/epjb/e2011-20162-6
Hyperbolic diffusion in chaotic systems
1
Department of Physical Chemistry and Technology of Polymers,
Section of Physical Chemistry and Biophysics, Silesian University of Technology, 44-100 Gliwice, Poland
2
Institute of Physics, University of Silesia, 40-007 Katowice, Poland
Corresponding author: a jerzy.luczka@us.edu.pl
Received:
4
March
2011
Revised:
23
May
2011
Published online:
23
September
2011
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.
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2011