Effective Bounds on Network-Size for Anti-phase Synchronization

TL;DR

This paper investigates the limits of anti-phase synchronization in coupled oscillators, linking it to combinatorial optimization and demonstrating its rarity and constraints in real-world networks.

Contribution

It establishes effective bounds on network size for anti-phase synchronization and connects it to the Ising model and Steiner-tree problem.

Findings

Anti-phase synchronization is less frequent than in-phase in real networks.

There are explicit bounds on the number of oscillators that can anti-phase synchronize.

The study links anti-phase synchronization to combinatorial optimization problems.

Abstract

We consider anti-phase synchronization of coupled oscillators using the Stuart-Landau model and explore its relative infrequency in occurrence compared to in-phase synchronization. We report effective limits in number of oscillators which can anti-phase synchronize for general configurations of real-world networks. We link anti-phase synchronization to the Ising model and consequently to combinatorial optimization problems, thereby explaining experimentally observed limits in self-organization of natural systems. We illustrate this using the Steiner-tree problem.