Crowd dynamics of self-propelled individuals with collision avoidance considering anticipation and intrusion aversion

Crowd motion represents a ubiquitous phenomenon across various contexts in reality, and has been extensively investigated at different scales. This paper aims to investigate order formation of the crowd driven by collision avoidance, examining the associated motion features. We introduce a parsimonious model incorporating collision avoidance with two characteristic directions, modulated by a ratio parameter p. Anticipation and intrusion aversion are incorporated to facilitate more advanced or sensitive responses to the proximity. The simulations were carried out in the wander and the gathering motion cases (in the absence of or with the specific target). The results reveal the transition from the chaotic state to the ordered state, manifested as the collective motion in the uniform direction or the synchronized rotation. Exploration of the parameter p-space unveils discontinuities in polarization transition, characterized by a sharp increase beyond a threshold p value. Both anticipation and intrusion aversion enhance avoidance behavior, yet the features can differ in the average speed and spatial arrangement within the ordered state. Intriguingly, with large intrusion aversion, the desire to keep larger distances from others may counterintuitively lead to a more uneven spatial distribution, with several individuals in close proximity.