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

Area of Science:

• Mathematical Biology
• Complex Systems
• Animal Behavior

Background:

• Bird flocking exhibits complex emergent behaviors, including synchronized directional changes.
• Existing models often rely on external stimuli or predefined leadership structures.
• Recent observations of starlings and jackdaws provide new insights into flock dynamics.

Purpose of the Study:

• To develop a minimal agent-based mathematical model for bird flocking.
• To simulate spontaneous, self-organized changes in flock direction.
• To explore emergent leadership in groups of indistinguishable agents.

Main Methods:

• Utilized a system of second-order delayed stochastic differential equations.
• Incorporated discontinuous functions in both space and time.
• Developed an agent-based model where each bird can initiate turns.
• Analyzed theoretical properties and performed numerical simulations.

Main Results:

• The model successfully reproduces spontaneous, self-organized changes in flock direction.
• Demonstrated that leadership can emerge dynamically within a group of identical agents.
• Simulations show emergent coordinated turning behaviors without external cues.

Conclusions:

• The proposed mathematical model offers a parsimonious explanation for complex flocking behaviors.
• Emergent leadership and spontaneous turns are key features of self-organized flock dynamics.
• This framework provides a novel perspective on collective behavior in biological systems.