Suppression of Quasiperiodicity in Circle Maps with Quenched Disorder

TL;DR

Introducing quenched disorder into circle maps suppresses quasiperiodicity in large systems, leading to dominant mode-locking and Arnold tongues, contrasting standard behavior.

Contribution

This paper demonstrates that quenched disorder causes the disappearance of quasiperiodic behavior in large circle maps, revealing a new understanding of their dynamics.

Findings

Quasiperiodicity fraction decreases with system size

Almost all realizations show mode-locking in the infinite limit

Parameter space is dominated by Arnold tongues

Abstract

We show that introducing quenched disorder into a circle map leads to the suppression of quasiperiodic behavior in the limit of large system sizes. Specifically, for most parameters the fraction of disorder realizations showing quasiperiodicity decreases with the system size and eventually vanishes in the limit of infinite size, where almost all realizations show mode-locking. Consequently, in this limit, and in strong contrast to standard circle maps, almost the whole parameter space corresponding to invertible dynamics consists of Arnold tongues.