UC Merced

Collective motion is a widespread phenomenon in nature where individuals actively propel themselves, gather together and move as a group. Some examples of collective motion are bird flocks, fish schools, bacteria swarms, cell clusters, and crowds of people. Many models seek to understand the effects of activity in collective systems including things such as environmental disorder, density, and interaction details primarily at infinite size limits and with uniform populations. In this dissertation I investigate the effects of finite sizes and behavioral heterogeneity as it exists in nature. Behavioral heterogeneity can originate from several different sources. Mixed populations of individuals can have inherently different behaviors such as mutant bacteria, injured fish, or agents that prefer individualistic behavior over coordinated motion. Alternatively, agents may modify their own behavior based on some local environmental dependency, such as local substrate, or density.

In cases such as mutant cheaters in bacteria or malfunctioning drones in swarms, mixed populations of behaviorally heterogeneous agents can be modelled as arising in the form of aligning and non-aligning agents. When this kind of heterogeneity is introduced, there is a critical carrying capacity of non-aligners above which the system is unable to form a cohesive ordered group. However, if the cohesion of the group is relaxed to allow for fracture, the system will actively sort out non-aligning agents the system will exist at a critical non-aligner fraction. A similar heterogeneity could result in a mixture of high and low noise individuals. In this case there is also a critical carry capacity beyond which the system is unable to reach an ordered state, however the nature of this transition depends on the model details.

Agents which are part of an ordered collective may vary their behavior as the group changes environments such as a flock of birds flying into a cloud. Using a unique model of a flock where the group behaves as a rigid disk reveals interesting behaviors as the system crosses a boundary between interfaces. The collective rotates and reorients or becomes stuck on the boundary as it crosses. I also investigate the effects of variable behavior depending on local density, and find that a frustration driven transient rotational phase arises in clusters where agents with low local density move faster than those with high local density as in cell clusters. All together I have shown that behavioral heterogeneity in collective motion can lead to unique phases and behaviors that are not seen in their homogeneous counterparts.