# Arnold tongues for a resonant injection-locked frequency divider: analytical and numerical results

## TL;DR

This paper analyzes the structure of Arnold tongues in a resonant injection-locked frequency divider, providing analytical formulas for their widths and extending previous results to more general cases.

## Contribution

It offers exact analytical expressions for Arnold tongue widths in a resonant frequency divider, enhancing understanding of frequency locking phenomena.

## Key findings

- Analytical formulas for Arnold tongue widths
- Numerical and experimental validation of results
- Extension to general driving terms

## Abstract

In this paper we consider a resonant injection-locked frequency divider which is of interest in electronics, and we investigate the frequency locking phenomenon when varying the amplitude and frequency of the injected signal. We study both analytically and numerically the structure of the Arnold tongues in the frequency-amplitude plane. In particular, we provide exact analytical formulae for the widths of the tongues, which correspond to the plateaux of the devil's staircase picture. The results account for numerical and experimental findings presented in the literature for special driving terms and, additionally, extend the analysis to a more general setting.