1999/11/25 by Uǧur Tırnaklı, Ugur Tirnakli · 3 citations
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Complex Systems and Time Series Analysis #Fractional Differential Equations Solutions #Statistical Mechanics and Entropy #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.62.7857
published as Phys. Rev. E 62 (2000) 7857 · 6 pages with 3 figs
arxiv created 1999/11/25 · openalex publication_date 2000/12/01 · arxiv updated 2010/06/14 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
In this study, using q-generalized bit cumulants (q is the nonextensivity parameter of the recently introduced Tsallis statistics), we investigate the asymmetric unimodal maps xt+1=1\ensuremath-a|xt|^zi (i=1,2 correspond to xt>0 and xt<0, respectively; zi>1, 0<a<~2, t=0,1,2,…). The study of the q-generalized second cumulant C2(q) of these maps allows us to determine the dependence of the nonextensivity parameter q on the inflection parameter pairs (z1,z2). The slope of the C2(q) versus C2(1) plot (where C2(1) is the standard second cumulant) provides the necessary tool to accomplish this task. The slope behaves exactly the same as the proper q values (say q*) that were obtained for logisticlike maps (z1=z2=z) by Costa et al. [Phys. Rev. E 56, 245 (1997)]. It appears that as z2\ensuremath-z1\ensuremath→\ifmmode±\else\textpm\fi\ensuremath∞ this slope approaches unity. This behavior is very similar to the behavior of q* as a function of the inflection parameter for some z-dependent maps; namely, as \stackrel\ensuremath→z\ensuremath∞, q* approaches 1.