Asymmetric Unimodal Maps: Some Results from q-generalized Bit Cumulants

TL;DR

This paper explores the behavior of asymmetric unimodal maps using q-generalized bit cumulants from Tsallis statistics, revealing how their inflexion parameters depend on the nonextensivity parameter q, similar to logistic-like maps.

Contribution

It introduces the analysis of asymmetric unimodal maps through q-generalized cumulants, establishing their parameter dependence on q for the first time.

Findings

Inflexion parameters depend on q in a manner similar to logistic maps.

The behavior of asymmetric unimodal maps parallels that of logistic-like maps.

First-time characterization of these maps using q-generalized cumulants.

Abstract

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. The study of the q-generalized second cumulant of these maps allows us to determine, for the first time, the dependence of the inflexion paremeter pairs (z_1,z_2) to the nonextensivity parameter q. This behaviour is found to be very similar to that of the logistic-like maps (z_1=z_2=z) reported recently by Costa et al. [Phys.Rev.E 56 (1997) 245].