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Statistical descriptions of nonlinear systems at the onset of chaos

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  • Coraddu, Massimo
  • Lissia, Marcello
  • Tonelli, Roberto

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.

Suggested Citation

  • Coraddu, Massimo & Lissia, Marcello & Tonelli, Roberto, 2006. "Statistical descriptions of nonlinear systems at the onset of chaos," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 365(1), pages 252-257.
    • Handle: RePEc:eee:phsmap:v:365:y:2006:i:1:p:252-257
    DOI: 10.1016/j.physa.2006.01.007
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    Keywords

    Statistics; Chaos; Entropy;
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