Sensitivity function and entropy increase rates for z-logistic map family at the edge of chaos

Details Sensitivity function and entropy increase rates for z-logistic map family at the edge of chaos Sensitivity function and entropy increase rates for z-logistic map family at the edge of chaos

2006-03-09

arxiv.org/abs/cond-mat/0603245v1

Physics

Condensed Matter

Statistical Mechanics

9 pages, 2 figs

Scientific paper

10.1016/j.physa.2006.08.008

It is well known that, for chaotic systems, the production of relevant entropy (Boltzmann-Gibbs) is always linear and the system has strong (exponential) sensitivity to initial conditions. In recent years, various numerical results indicate that basically the same type of behavior emerges at the edge of chaos if a specific generalization of the entropy and the exponential are used. In this work, we contribute to this scenario by numerically analysing some generalized nonextensive entropies and their related exponential definitions using $z$-logistic map family. We also corroborate our findings by testing them at accumulation points of different cycles.

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