System size synchronization

TL;DR

This paper introduces a novel form of synchronization in complex systems where the system size influences the locking of output frequency to an external drive, characterized by a deep minimum in phase diffusion at certain sizes.

Contribution

The work identifies and characterizes system size synchronization, a new phenomenon linking system size to synchronization behavior in stochastic coupled units.

Findings

Existence of a deep minimum in phase diffusion coefficient at specific system sizes.

Output frequency locks to external frequency over a range of system sizes.

Analytical and numerical methods successfully describe the synchronization phenomenon.

Abstract

In this work we bring out the existence of a novel kind of synchronization associated to the size of a complex system. A dichotomic random jump process associated to the dynamics of an externally driven stochastic system with $N$ coupled units is constructed. We define an output frequency and phase diffusion coefficient. System size synchronization occurs when the average output frequency is locked to the external one and the average phase diffusion coefficient shows a very deep minimum for a range of system sizes. Analytical and numerical procedures are introduced to study the phenomenon, and the results describe successfully the existence of system size synchronization.