Information transfer enhanced by non-reciprocity in a model of turning flocks

TL;DR

This paper introduces an active torque component into a flock model, enhancing information transfer speed and efficiency during turning events, and reveals a non-reciprocal modified Korteweg-de Vries equation governing the system.

Contribution

It extends existing flock models by incorporating active torques, demonstrating their role in improving information transfer and introducing non-reciprocity.

Findings

Active torques increase information transfer speed during turns.

The model predicts non-reciprocal information flow in flocks.

The continuum limit yields a non-reciprocal mKdV equation with dissipation.

Abstract

Seminal works on animal collectives started proposing a diffusive model (overdamped) for the information transfer occurring in it \cite{Vicsek}. Afterwards, the introduction of self-rotational inertia brought into play an underdamped model able to better describe the information flux occurring in a real tuning flock event \cite{Atta}. That model was recently improved by adding nonlinear torques which allowed to match experiments \cite{cavagna2025}. The current work extends the latter model by adding active torques to a one-dimensional flock of boids (bird-like objects) while keeping key ingredients such as self-rotational inertia and nonlinearity. Those active torques are seen to enhance the system's information transfer speed and efficiency during a turning event, as well as rendering it a non-reciprocal status. The proposed internal active torques are motivated by the adaptive injection of rotational energy (active system) of birds in a real flock while turning. The continuum limit of the proposed model leads to a non-reciprocal modified Korteweg-de Vries (mKdV) equation with dissipation, whose structure allows the information transfer speed to be a function of the turning angular velocity. This feature occurs in real birds since under threat, birds turn faster and are required to get the information more rapid to keep cohesion.