Statistical descriptions of nonlinear systems at the onset of chaos

Massimo Coraddu, Marcello Lissia and Roberto Tonelli

Physica A: Statistical Mechanics and its Applications, 2006, vol. 365, issue 1, 252-257

Abstract: Ensemble of initial conditions for nonlinear maps can be described in terms of entropy. This ensemble entropy shows an asymptotic linear growth with rate K. The rate K matches the logarithm of the corresponding asymptotic sensitivity to initial conditions λ. The statistical formalism and the equality K=λ can be extended to weakly chaotic systems by suitable and corresponding generalizations of the logarithm and of the entropy. Using the logistic map as a test case we consider a wide class of deformed statistical description which includes Tsallis, Abe and Kaniadakis proposals. The physical criterion of finite-entropy growth K strongly restricts the suitable entropies. We study how large is the region in parameter space where the generalized description is useful.

Keywords: Statistics; Chaos; Entropy (search for similar items in EconPapers)
Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:365:y:2006:i:1:p:252-257

DOI: 10.1016/j.physa.2006.01.007

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