Mean Field and Mean Ensemble Frequencies of a System of Coupled Oscillators

TL;DR

This paper studies systems of coupled oscillators with asymmetries, revealing that their mean ensemble and entrainment frequencies can differ significantly, even surpassing natural frequency limits, impacting understanding of real cooperative systems.

Contribution

It demonstrates that mean ensemble frequency can differ from entrainment frequency in asymmetric oscillator systems, highlighting the importance of distinguishing these variables.

Findings

Mean ensemble frequency can differ from entrainment frequency.

Frequencies can lie beyond natural frequency limits.

Results have implications for real systems with parameter distributions.

Abstract

We investigate interacting phase oscillators whose mean field is at a different frequency from the mean or mode of their natural frequencies. The associated asymmetries lead to a macroscopic travelling wave. We show that the mean ensemble frequency of such systems differs from their entrainment frequency. In some scenarios these frequencies take values that, counter-intuitively, lie beyond the limits of the natural frequencies. The results indicate that a clear distinction should be drawn between the two variables describing the macroscopic dynamics of cooperative systems. This has important implications for real systems where a non-trivial distribution of parameters is common.