Central limit behavior of deterministic dynamical systems

Details Central limit behavior of deterministic dynamical systems Central limit behavior of deterministic dynamical systems

2007-01-25

arxiv.org/abs/cond-mat/0701622v6

Phys. Rev. E 75, 040106(R) (2007)

Physics

Condensed Matter

Statistical Mechanics

6 pages, 5 figures

Scientific paper

10.1103/PhysRevE.75.040106

We investigate the probability density of rescaled sums of iterates of deterministic dynamical systems, a problem relevant for many complex physical systems consisting of dependent random variables. A Central Limit Theorem (CLT) is only valid if the dynamical system under consideration is sufficiently mixing. For the fully developed logistic map and a cubic map we analytically calculate the leading-order corrections to the CLT if only a finite number of iterates is added and rescaled, and find excellent agreement with numerical experiments. At the critical point of period doubling accumulation, a CLT is not valid anymore due to strong temporal correlations between the iterates. Nevertheless, we provide numerical evidence that in this case the probability density converges to a $q$-Gaussian, thus leading to a power-law generalization of the CLT. The above behavior is universal and independent of the order of the maximum of the map considered, i.e. relevant for large classes of critical dynamical systems.

Affiliated with

Also associated with

No associations

Rating

Central limit behavior of deterministic dynamical systems 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 Central limit behavior of deterministic dynamical systems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Central limit behavior of deterministic dynamical systems will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-328674