Müller-Bender D, Kastner JL, Radons G. Suppression of quasiperiodicity in circle maps with quenched disorder.
Phys Rev E 2022;
106:L012202. [PMID:
35974539 DOI:
10.1103/physreve.106.l012202]
[Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/20/2022] [Accepted: 06/27/2022] [Indexed: 06/15/2023]
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.
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