Hyperbolic diffusion in chaotic systems

被引：1

作者：

Borys, P. ^{[1
]}

Grzywna, Z. J. ^{[1
]}

Luczka, J. ^{[2
]}

机构：

[1] Silesian Tech Univ, Dept Phys Chem & Technol Polymers, Sect Phys Chem & Biophys, PL-44100 Gliwice, Poland

[2] Univ Silesia, Inst Phys, PL-40007 Katowice, Poland

来源：

EUROPEAN PHYSICAL JOURNAL B | 2011年 / 83卷 / 02期

关键词：

ANOMALOUS DIFFUSION; RANDOM-WALKS; TRANSPORT; EQUATIONS; DRIVEN; MODELS; ORIGIN; MARKOV;

D O I：

10.1140/epjb/e2011-20162-6

中图分类号：

O469 [凝聚态物理学];

学科分类号：

070205 ;

摘要：

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.

引用

页码：223 / 233

页数：11

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