2025/03/03 by Lama, Andrea, di Bernardo, Mario, Klapp, Sabine H. L. · 2 citations
#Adaptation and Self-Organizing Systems (nlin.AO) #FOS: Physical sciences #Soft Condensed Matter (cond-mat.soft)
paper · doi:10.48550/arxiv.2503.01112
Field theories for complex systems traditionally focus on collective behaviors emerging from simple, reciprocal pairwise interaction rules. However, many natural and artificial systems exhibit behaviors driven by microscopic decision-making processes that introduce both nonreciprocity and many-body interactions, challenging these conventional approaches. We develop a theoretical framework to incorporate decision-making into field theories using the shepherding control problem as a paradigmatic example of a multi-agent control system, where agents (herders) must coordinate to confine another group of agents (targets) within a prescribed region. By introducing continuous approximations of two key decision-making elements - target selection and trajectory planning - we derive field equations that capture the essential features of this distributed control problem. Our theory reveals that different decision-making strategies emerge at the continuum level, from average attraction to highly selective choices, and from undirected to goal-oriented motion, driving transitions between homogeneous and confined configurations. The resulting nonreciprocal field theory not only describes the shepherding problem but provides a general framework for incorporating decision-making into continuum theories of collective behavior, with implications for applications ranging from robotic swarms to crowd management systems.