Multistable behavior above synchronization in a locally coupled Kuramoto model

TL;DR

This paper investigates the complex multistable behaviors of a ring of coupled oscillators modeled after Kuramoto, revealing diverse solutions and their evolution above the synchronization threshold within a specific solvability region.

Contribution

It introduces a detailed analysis of solution multiplicity and phase space structure in a locally coupled Kuramoto model above critical synchronization.

Findings

Multiple solutions exist within the solvability region.

Solutions exhibit different characteristics depending on boundary sections.

The evolution of solutions with increasing coupling is characterized.

Abstract

A system of nearest neighbors Kuramoto-like coupled oscillators placed in a ring is studied above the critical synchronization transition. We find a richness of solutions when the coupling increases, which exists only within a solvability region (SR). We also find that they posses different characteristics, depending on the section of the boundary of the SR where the solutions appear. We study the birth of these solutions and how they evolve when {K} increases, and determine the diagram of solutions in phase space.