# A Coupled Oscillator Model for the Origin of Bimodality and Multimodality

## TL;DR

This paper demonstrates that bimodal and multimodal distributions can naturally arise from repulsive coupling in oscillator models, challenging the assumption that natural distributions are typically unimodal.

## Contribution

It introduces a rigorous analysis of how multimodality emerges from inhibitory coupling in variants of the Kuramoto model, expanding understanding of distribution shapes in coupled systems.

## Key findings

- Multimodality can result from repulsive coupling dynamics.
- The analysis applies broadly to various coupling functions.
- Multimodal distributions emerge naturally in oscillator systems.

## Abstract

Perhaps because of the elegance of the central limit theorem, it is often assumed that distributions in nature will approach singly-peaked, unimodal shapes reminiscent of the Gaussian normal distribution. However, many systems behave differently, with variables following apparently bimodal or multimodal distributions. Here we argue that multimodality may emerge naturally as a result of repulsive or inhibitory coupling dynamics, and we show rigorously how it emerges for a broad class of coupling functions in variants of the paradigmatic Kuramoto model.