Frequency Precision of Two-Dimensional Lattices of Coupled Oscillators with Spiral Patterns

Abstract

Two-dimensional lattices of N synchronized oscillators with reactive coupling are considered as high-precision frequency sources in the case where a spiral pattern is formed. The improvement of the frequency precision is shown to be independent of N for large N, unlike the case of purely dissipative coupling where the improvement is proportional to N, but instead depends on just those oscillators in the core of the spiral that acts as the source region of the waves. Our conclusions are based on numerical simulations of up to N=29929 oscillators, and analytic results for a continuum approximation to the lattice in an infinite system. We derive an expression for the dependence of the frequency precision on the reactive component of the coupling constant, depending on a single parameter given by fitting the frequency of the spiral waves to the numerical simulations.

7 pages, 6 figures

References in corpus (4)

• A Passive Phase Noise Cancellation Element
• Improving the Frequency Precision of Oscillators by Synchronization
• Collective fluctuations in networks of noisy components
• Perturbation Analysis of the Kuramoto Phase Diffusion Equation Subject to Quenched Frequency Disorder

Cited by in corpus (5)

• Pattern phase diagram for 2D arrays of coupled limit-cycle oscillators
• Collective phase dynamics of globally coupled oscillators: Noise-induced anti-phase synchronization
• From Kardar-Parisi-Zhang scaling to explosive desynchronization in arrays of limit-cycle oscillators
• Phase-locked Patterns of the Kuramoto Model on 3-Regular Graphs
• Phase synchronization between collective rhythms of fully locked oscillator groups