Collective Dynamics in Physical and Social Networks

Abstract

We study four systems where individual units come together to display a range of collective behavior. First, we consider a physical system of phase oscillators on a network that expands the Kuramoto model to include oscillator-network interactions and the presence of noise: using a Hebbian-like learning rule, oscillators that synchronize in turn strengthen their connections to each other. We find that the average degree of connectivity strongly affects rates of flipping between aligned and anti-aligned states, and that this result persists to the case of complex networks. Turning to a fully multi-player, multi-strategy evolutionary dynamics model of cooperating bacteria that change who they give resources to and take resources from, we find several regimes that give rise to high levels of collective structure in the resulting networks. In this setting, we also explore the conditions in which an intervention that affects cooperation itself (e.g. “seeding the network with defectors”) can lead to wiping out an infection. We find a non-monotonic connection between the percent of disabled cooperation and cure rate, suggesting that in some regimes a limited perturbation can lead to total population collapse. At a larger scale, we study how the locomotor system recovers after amputation in fruit flies. Through experiment and a theoretical model of multi-legged motion controlled by neural oscillators, we find that proprioception plays a role in the ability of flies to control leg forces appropriately to recover from a large initial turning bias induced by the injury. Finally, at the human scale, we consider a social network in a traditional society in Africa to understand how social ties lead to group formation for collective action (stealth raids). We identify critical and distinct roles for both leadership (important for catalyzing a group) and friendship (important for final composition). We conclude with prospects for future work.