Universal dynamics of spatiotemporal entrainment with phase symmetry

TL;DR

This paper investigates the universal principles governing how localized patterns synchronize with external signals, especially when internal symmetries are broken, using the complex-Ginzburg-Landau model as a case study.

Contribution

It derives a universal locking dynamical system for patterns with broken internal phase symmetry, revealing the structure of entrainment across different systems.

Findings

Universal locking dynamics are governed by the internal symmetry group.

Explicit calculation of locking domains for complex-Ginzburg-Landau solitons.

Entrainment behavior depends on the symmetry-breaking structure.

Abstract

We study the entrainment of a localized pattern by an external signal via its coupling to zero modes associated with broken symmetries. We show that when internal symmetries are broken, entrainment is governed by a multi-degree of freedom locking dynamical system that has a universal structure defined by the internal symmetry group and its breaking. We derive explicitly the universal locking dynamics for entrainment of patterns breaking internal phase symmetry, and calculate the locking domains and the entrainment structure for the example of complex-Ginzburg-Landau solitons.