Circular motion subject to external alignment under active driving: nonlinear dynamics and the circle map

TL;DR

This paper investigates the nonlinear dynamics of self-propelled objects that move in discrete steps with directional adjustments, revealing complex behaviors like chaos and period doubling affecting their trajectories and collective motion.

Contribution

It introduces a model combining discrete step motion with angular alignment, analyzing the resulting nonlinear dynamics and chaotic behaviors in active driving systems.

Findings

Nonlinear dynamics include period doubling and chaos.

Angular overreaction influences trajectory complexity.

Collective motion exhibits effects of nonlinear individual dynamics.

Abstract

Hardly any real self-propelling or actively driven object is perfect. Thus, undisturbed motion will generally not follow straight lines but rather circular trajectories. We here address self-propelled or actively driven objects that move in discrete steps and additionally tempt to migrate towards a certain direction by discrete angular adjustment. Overreaction in the angular alignment is possible. This competition implies pronounced nonlinear dynamics including period doubling and chaotic behavior in a broad parameter regime. Such behavior directly affects the appearance of the trajectories, also during collective motion under spatial self-concentration.