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

TL;DR

This paper investigates how two-dimensional lattices of coupled oscillators with spiral patterns can serve as high-precision frequency sources, showing that frequency accuracy depends mainly on the spiral core rather than the total number of oscillators.

Contribution

It demonstrates that frequency precision improvement in spiral-patterned oscillator lattices is independent of system size and depends primarily on the core region, supported by simulations and continuum analysis.

Findings

Frequency precision is independent of N for large lattices.

Core oscillators determine the frequency accuracy.

Analytic expression relates frequency precision to coupling parameters.

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.