Universality in Globally Coupled Maps and Flows

TL;DR

This paper demonstrates that universality observed in chaotic elements extends to complex systems like coupled flows, revealing similar bifurcation behaviors and dynamic patterns such as synchronized clusters and dancing quasi-clusters.

Contribution

It introduces a globally coupled Flow lattice (GCFL) as an analog to GCML and explores its universal chaotic behaviors and cluster dynamics.

Findings

Duffing GCFL exhibits bifurcation behavior similar to GCML.

Lorenz GCFL shows two quasi-clusters in opposite phase motion.

Complex flow systems can display universal chaotic phenomena.

Abstract

We show that universality in chaotic elements can be lifted to that in complex systems. We construct a globally coupled Flow lattice (GCFL), an analog of a globally coupled Map lattice (GCML). We find that Duffing GCFL shows the same behavior with GCML; population ratio between synchronizing clusters acts as a bifurcation parameter. Lorenz GCFL exhibits interesting two quasi-clusters in an opposite phase motion. Each of them looks like Will o' the wisp; they dance around in opposite phase.