Simulating the interactions with boundaries and barriers in collective motion models

Collective motion and behavior is a common phenomenon that can be seen across a variety of biological systems that range in scale from cells moving within living organisms, crowds of people interacting within thoroughfares, through to herds of large mammals. Interactions between these individual entities and their environment can give rise to spectacular, self-organizing, visual displays that emerge in the absence of any apparent centralized control. There have been many studies that reproduce his phenomena by describing the movement patterns in terms of the rules that govern the interactions between individuals participating in the collective behavior. The most common approach used in these simulations consists of a zone-based model, where individuals move away from others close by (i.e. repulsion to avoid collision) and align and/or move towards individuals at greater distances to maintain the direction and level of cohesion observed. The application of this relatively simple scheme has proven sufficient to generate simulated output that has been successfully matched to observable measures from experimental data such as polarization, rotation, turning rates, total group area and distributions of nearest neighbors.