Regular and irregular modulation of frequencies in limit cycle oscillator networks

TL;DR

This paper investigates how limit cycle oscillator networks exhibit both regular and irregular frequency modulations driven by amplitude changes, revealing mechanisms and network influences behind these complex behaviors.

Contribution

It introduces a detailed analysis of frequency distribution and modulation mechanisms in limit cycle oscillator networks, highlighting the role of network topology.

Findings

Networks show stationary frequency distributions at regular intervals.

Frequencies can undergo continuous irregular modulation.

Network topology influences frequency modulation behaviors.

Abstract

Frequency modulation by perturbation is the essential trait that differentiates limit cycle oscillators from phase oscillators. We studied networks of identical limit cycle oscillators whose frequencies are modulated sensitively by the change of their amplitudes, and demonstrated that the frequencies sustainably take distributed values. We observed two complex phenomena in the networks: stationarily distributed frequencies at a regular interval, and continuous irregular modulation of frequencies. In the analysis we reveal the mechanisms by which the frequencies are distributed, and show how the sensitive modulation of frequencies produces these complex phenomena. We also illustrate the topology of networks regulating the behaviors of the systems.