An all-leader agent-based model for turning and flocking birds

TL;DR

This paper introduces a novel agent-based model for bird flocking that captures spontaneous directional changes and emergent leadership among indistinguishable agents, based on second-order stochastic differential equations.

Contribution

The model uniquely allows any bird to initiate turns, demonstrating emergent leadership without external stimuli, advancing understanding of collective animal behavior.

Findings

Model reproduces spontaneous flock turning behavior

Leadership emerges among identical agents without external cues

Numerical simulations support theoretical properties

Abstract

Starting from recent experimental observations of starlings and jackdaws, we propose a minimal agent-based mathematical model for bird flocks based on a system of second-order delayed stochastic differential equations with discontinuous (both in space and time) right-hand side. The model is specifically designed to reproduce self-organized spontaneous sudden changes of direction, not caused by external stimuli like predator's attacks. The main novelty of the model is that every bird is a potential turn initiator, thus leadership is formed in a group of indistinguishable agents. We investigate some theoretical properties of the model and we show the numerical results. Biological insights are also discussed.