Transfer entropy on collective motion with undeclared loose leader–follower (LLF) structure

Abstract

During an emergency or evacuation, individuals focus on the movement of their neighbors and follow those in sight, even without social affiliation, forming the undeclared Loose Leader-Follower (LLF) group, rather than the usual assumption of following certain rules in most of evacuation models. Inspired by the real-life experience and experimental data, the study develops a novel stochastic process-based evacuation model, integrated the LLF structure in collective motion to clarify the mechanism underlying individual interaction and refine the walking process according to attainable information. Transfer entropy (TE), a model-free measure of the direction of information flow, is used to detect the role of the individuals in the LLF structure from the time-series reconstructed motion information (e.g., the walking coordinate series). To reduce the error of the role detection, according to the 3σ principle for TE values, the detection threshold is decided based on the surrogate walking data. For simulation of their motion decision in the LLF structure, the TE is integrated into the walking behavior mode (TE-POMDP) using the Partially Observable Markov Decision Process (POMDP), that produces their motion behavior under the typical attained information condition. The results show that the TE-POMDP can provide more realistic trajectories. Additionally, we find that a ‘Delta-like’ formation of leading group distribution was presented and remained stable in the procession after a short period of confusion in early stage.