Parallels between the dynamics at the noise-perturbed onset of chaos in logistic maps and the dynamics of glass formation

摘要

We develop the characterization of the dynamics at the noise-perturbed edge of chaos in logistic maps in terms of the quantities normally used to describe glassy properties in structural glass formers. Following the recognition [Phys. Lett. A 328, 467 (2004)] that the dynamics at this critical attractor exhibits analogies with that observed in thermal systems close to vitrification, we determine the modifications that take place with decreasing noise amplitude in ensemble- and time-averaged correlations and in diffusivity. We corroborate explicitly the occurrence of two-step relaxation, aging with its characteristic scaling property, and subdiffusion and arrest for this system. We also discuss features that appear to be specific to the map.