Aging at the edge of chaos: Glassy dynamics and nonextensive statistics

TL;DR

This paper demonstrates that the dynamics at the edge of chaos in noisy logistic maps exhibit glassy features like aging and two-step relaxation, modeled using nonextensive statistics and analytical q-exponentials.

Contribution

It reveals that noise-perturbed chaos in logistic maps mimics glassy dynamics and employs nonextensive statistics for analytical description.

Findings

Glassy dynamics features appear at the chaos threshold.

Relaxation dynamics are described by q-exponentials.

Nonextensive statistics effectively model the observed phenomena.

Abstract

We go over our finding that the dynamics at the noise-perturbed edge of chaos in logistic maps is comparable to that observed in supercooled liquids close to vitrification. That is, the three major features of glassy dynamics in structural glass formers, two-step relaxation, aging, and a relationship between relaxation time and configurational entropy, are displayed by orbits with vanishing Lyapunov exponent. The known properties in control-parameter space of the noise-induced bifurcation gap play a central role in determining the characteristics of dynamical relaxation at the chaos threshold. Time evolution is obtained from the Feigenbaum RG transformation, it is expressed analytically via q-exponentials, and described in terms of nonextensive statistics. Key words: Glassy dynamics, ergodicity breakdown, edge of chaos, external noise, nonextensive statistics