Suppression of Quasiperiodicity in Circle Maps with Quenched Disorder

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.

arXiv comment7 pages, 4 figures; minor changes due to review process

References in corpus (17)

• Annealed and quenched limit theorems for random expanding dynamical systems
• Anomalous transport: a deterministic approach
• Laminar Chaos
• Fractal structures of normal and anomalous diffusion in nonlinear nonhyperbolic dynamical systems
• Theory of Circle Maps and the Problem of One-Dimensional Optical Resonator with a Periodically Moving Wall
• Universality in Three-Frequency Resonances
• Negative and Nonlinear Response in an Exactly Solved Dynamical Model of Particle Transport
• From dynamical systems with time-varying delay to circle maps and Koopmanism
• Real bounds and Lyapunov exponents
• Dynamical Casimir effect in a periodically changing domain: A dynamical systems approach
• Laminar Chaos in experiments and nonlinear delayed Langevin equations: A time series analysis toolbox for the detection of Laminar Chaos
• Deterministic Walks in Quenched Random Environments of Chaotic Maps
• On stochastic differential equations with random delay
• Arnold maps with noise: Differentiability and non-monotonicity of the rotation number
• The dynamics of a driven harmonic oscillator coupled to independent Ising spins in random fields
• A family of rotation numbers for discrete random dynamics on the circle
• Lyapunov exponent of random dynamical systems on the circle