Using a phase space cross section to study large complex systems

TL;DR

This paper introduces a phase space cross section method to analyze large coupled nonlinear systems, revealing fractal boundaries in phase and parameter space that characterize transitions in synchronization behavior.

Contribution

The paper proposes a novel phase space reduction technique for large systems, enabling visualization of complex transitions and fractal boundary analysis.

Findings

Transitions between synchronization phases can be fractal

Phase space cross section reveals complex boundary structures

Method applied successfully to coupled map systems

Abstract

For large coupled nonlinear systems, it is difficult to visualize the high-dimensional phase space, which has been thoroughly studied in smaller systems with regards to phenomena such as riddled basins. Here we propose a method to reduce the phase space by defining a phase space cross section. The method is applied to a system of dynamically coupled maps introduced by Ito & Kaneko (Phys. Rev. Lett., 88, 028701, 2001 & Phys. Rev. E, 67, 046226, 2003). We show that the transitions between phases of different synchronization behaviour are not always sharp but can be characterized by fractal boundaries in both phase and parameter space.