Unexpected stray attractors in confined leader-follower dynamics driven by cone-of-vision interactions

Area of Science:

• Collective behavior
• Mathematical modeling
• Dynamical systems

Background:

• Fish schooling and leadership behaviors are complex phenomena observed in social groups.
• Mathematical models are crucial for understanding and replicating these intricate social dynamics.

Purpose of the Study:

• To explore social dynamics and evasion behaviors within confined groups using mathematical models.
• To investigate the likelihood of an individual permanently evading a cohesive group under controlled conditions.

Main Methods:

• Developed and utilized sophisticated mathematical models based on leader-follower configurations.
• Simulated interactions within a circular domain, incorporating cone-of-vision driven dynamics.
• Analyzed the resulting dynamical system for non-aligned, straying follower states and their transitions.

Main Results:

• Identified a rich supply of 'follower' states exhibiting chaotic intermittency between boundary following and long flights.
• Mapped these stray states in configuration space and explored transitions between them.
• Demonstrated robustness of observed behaviors through model variations and alternate leader trajectories.

Conclusions:

• A model stray fish's behavior mirrors a self-organized school responding to a point leader.
• Results have implications for dynamical systems with discontinuities, robotics, and understanding human behavior under confinement and normative control.