Swarming Lattice in Frustrated Vicsek-Kuramoto Systems

TL;DR

This paper introduces a frustration parameter into Vicsek-Kuramoto systems, revealing a transition from synchronized states to lattice formations driven by bifurcations, highlighting the sufficiency of orientational interactions for lattice emergence.

Contribution

The study demonstrates that purely orientational interactions can induce symmetric lattice formations in active matter, challenging the belief that spatial forces are necessary.

Findings

Transition to resting hexagonal lattice beyond critical frustration

Lattice formation governed by coupling strength and interaction radius

Orientational interactions alone can produce symmetric lattices

Abstract

We introduce a frustration parameter $\alpha$ into the Vicsek-Kuramoto systems of self-propelled particles. While the system exhibits conventional synchronized states, such as global phase synchronization and swarming, for low frustration ($\alpha < \pi/2$), beyond the critical point $\alpha = \pi/2$, a Hopf-Turing bifurcation drives a transition to a resting hexagonal lattice, accompanied by spatiotemporal patterns such as vortex lattices and dual-cluster lattices with oscillatory unit-cell motions. Lattice dominance is governed by coupling strength and interaction radius, with a clear parametric boundary balancing pattern periodicity and particle dynamics. Our results demonstrate that purely orientational interactions are sufficient to form symmetric lattices, challenging the necessity of spatial forces and illuminating the mechanisms driving lattice formation in active matter systems.