Ensemble averages and nonextensivity at the edge of chaos of one-dimensional maps

Details Ensemble averages and nonextensivity at the edge of chaos of one-dimensional maps Ensemble averages and nonextensivity at the edge of chaos of one-dimensional maps

2004-01-15

arxiv.org/abs/cond-mat/0401276v1

Physics

Condensed Matter

Statistical Mechanics

5 pages, 5 figures

Scientific paper

10.1103/PhysRevLett.93.020601

Ensemble averages of the sensitivity to initial conditions $\xi(t)$ and the entropy production per unit time of a {\it new} family of one-dimensional dissipative maps, $x_{t+1}=1-ae^{-1/|x_t|^z}(z>0)$, and of the known logistic-like maps, $x_{t+1}=1-a|x_t|^z(z>1)$, are numerically studied, both for {\it strong} (Lyapunov exponent $\lambda_1>0$) and {\it weak} (chaos threshold, i.e., $\lambda_1=0$) chaotic cases. In all cases we verify that (i) both $<\ln_q \xi > [\ln_q x \equiv (x^{1-q}-1)/(1-q); \ln_1 x=\ln x]$ and $ [S_q \equiv (1-\sum_i p_i^q)/(q-1); S_1=-\sum_i p_i \ln p_i]$ {\it linearly} increase with time for (and only for) a special value of $q$, $q_{sen}^{av}$, and (ii) the {\it slope} of $<\ln_q \xi>$ and that of $$ {\it coincide}, thus interestingly extending the well known Pesin theorem. For strong chaos, $q_{sen}^{av}=1$, whereas at the edge of chaos, $q_{sen}^{av}(z)<1$.

Affiliated with

Also associated with

No associations

Rating

Ensemble averages and nonextensivity at the edge of chaos of one-dimensional maps does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Ensemble averages and nonextensivity at the edge of chaos of one-dimensional maps, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Ensemble averages and nonextensivity at the edge of chaos of one-dimensional maps will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-585193