A coupled oscillator model for the origin of bimodality and multimodality

Area of Science:

• Complex systems
• Theoretical physics
• Mathematical biology

Background:

• The central limit theorem often leads to the assumption of unimodal (single-peaked) distributions in nature.
• However, many natural systems display bimodal or multimodal (multiple-peaked) distributions, deviating from this expectation.

Purpose of the Study:

• To investigate the emergence of multimodal distributions in natural systems.
• To demonstrate that repulsive or inhibitory coupling dynamics can naturally lead to multimodality.
• To rigorously analyze these phenomena within variants of the Kuramoto model.

Main Methods:

• Analysis of coupling dynamics in theoretical models.
• Mathematical derivations for a broad class of coupling functions.
• Simulations and theoretical analysis of the Kuramoto model variants.

Main Results:

• Repulsive or inhibitory coupling dynamics are shown to be a natural cause of multimodality.
• The emergence of multimodal distributions is rigorously demonstrated for various coupling functions.
• The Kuramoto model serves as a paradigmatic framework to illustrate these findings.

Conclusions:

• Multimodality in natural distributions can arise from inherent repulsive or inhibitory interactions.
• These findings challenge the universal applicability of the Gaussian normal distribution in all natural systems.
• The Kuramoto model provides a robust framework for understanding the mechanisms behind complex distribution patterns.