Asymmetric unimodal maps: Some results fromq-generalized bit cumulants
Makaleler > Tam Makale · 2000
Yazarlar: Uğur TIRNAKLI
Physical Review E, SCI Expanded İndekslerine Giren Dergi, Uluslararası, Wos, 2000, cilt 62, ss 7857-7860
Özet
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 ${x}_{t+1}=1\ensuremath{-}a|{x}_{t}{|}^{{z}_{i}}$ $(i=1,2$ correspond to ${x}_{t}>0$ and ${x}_{t}<0,$ respectively; ${z}_{i}>1,$ $0<a<~2,$ $t=0,1,2,\dots{}).$ The study of the q-generalized second cumulant ${C}_{2}^{(q)}$ of these maps allows us to determine the dependence of the nonextensivity parameter q on the inflection parameter pairs ${(z}_{1}{,z}_{2}).$ The slope of the ${C}_{2}^{(q)}$ versus ${C}_{2}^{(1)}$ plot (where ${C}_{2}^{(1)}$ 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 ${(z}_{1}{=z}_{2}=z)$ by Costa et al. [Phys. Rev. E 56, 245 (1997)]. It appears that as ${z}_{2}\ensuremath{-}{z}_{1}\ensuremath{\rightarrow}\ifmmode\pm\else\textpm\fi{}\ensuremath{\infty}$ 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 $\stackrel{\ensuremath{\rightarrow}}{z}\ensuremath{\infty},$ ${q}^{*}$ approaches 1.