[Paper Review] Activity induced synchronization

Demian Levis, Ignacio Pagonabarraga+1 more|arXiv (Cornell University)|Feb 7, 2018

Nonlinear Dynamics and Pattern Formation3 citations

TL;DR

This paper proposes that self-propulsion induces macroscopic synchronization in active oscillators, enabling two novel phases: collective motion via mutual suppression of opposite chiralities (analogous to flocking), and chiral segregation into synchronized clusters. Unlike passive systems, this synchronization arises through a positive feedback loop between motility and phase coordination, enabling global order from purely local interactions in 2D systems.

ABSTRACT

Synchronization, the emergence of temporally coordinated behavior in large populations of interacting elements, occurs on many different length scales, from biological to social systems, generating phenomena like the unison flashing of fireflies, the collective firing of neurons and the coordinated motion of crowds of people falling into step on the London millennium bridge. Although synchronizing entities often self-propel, like fireflies, people, etc., the present understanding of synchronization applies mostly to immobile phase oscillators. Here, we show that self-propulsion qualitatively affects the synchronization of oscillators in a way that it is impossible in passive systems. This activity-induced macroscopic synchronization generates two novel phases: one where oscillators of opposite chirality, rotating clock-wise or anti-clockwise, mutually suppress their rotations and cooperate to move collectively along a given direction, akin to the celebrated homogeneous flocking phase in active matter; and a second phase where oscillators segregate accordingly to their chirality and form synchronized macroscopic clusters. In both phases, self-propulsion supports synchronization via a positive feedback loop involving motility, a mechanism which is absent in traditional (static or dynamic) networks of oscillators and induces macroscopic synchronization in a 2D system with purely local interactions.

Motivation & Objective

• To understand how self-propulsion alters synchronization dynamics in oscillator populations compared to passive systems.
• To identify new macroscopic synchronization phases induced by activity in 2D systems with local interactions.
• To reveal the role of motility as a positive feedback mechanism in achieving global synchronization without global coupling.

Proposed method

• Modeling self-propelled oscillators using a minimal active matter framework with local interactions.
• Introducing chirality (clockwise vs. counterclockwise rotation) as a key variable in the oscillator dynamics.
• Simulating the system in 2D to observe emergent collective behavior under varying activity levels.
• Analyzing phase transitions via order parameters measuring synchronization and collective motion.
• Identifying feedback loops between motility and phase alignment as the driver of macroscopic order.
• Comparing results to passive oscillator models to isolate the effects of self-propulsion.

Experimental results

Research questions

• RQ1 How does self-propulsion alter the emergence of synchronization in oscillator populations compared to passive systems?
• RQ2 What novel collective phases arise due to activity in 2D systems with purely local interactions?
• RQ3 Can motility serve as a positive feedback mechanism to sustain global synchronization in active oscillator networks?
• RQ4 How do oscillators of opposite chirality interact under activity, and what emergent behaviors result?
• RQ5 What is the role of local interactions in enabling macroscopic synchronization when oscillators are self-propelled?

Key findings

• Self-propulsion enables a novel synchronization phase where oscillators of opposite chirality mutually suppress rotation and coherently move in a single direction, resembling homogeneous flocking.
• A second distinct phase emerges where oscillators segregate by chirality and form synchronized macroscopic clusters.
• The synchronization is sustained by a positive feedback loop between motility and phase alignment, absent in passive oscillator networks.
• Global synchronization is achieved in 2D systems with only local interactions, challenging the conventional need for global coupling.
• The mechanism is robust and qualitatively different from traditional synchronization in static or dynamic networks.
• The results demonstrate that activity alone can drive macroscopic order without external control or long-range interactions.