Abstract
Collective dynamics underpin many diverse complex systems e.g., animals, hu mans, and robotic multi-agent systems where a large number of individuals co operate. The information that allows for such collective behaviors to emerge flows through an interaction network specific to the ongoing process. Natu rally, this yields an intricate interplay between the collective dynamics on the one hand and the features of the interaction network on the other. Therefore, it is of paramount importance to understand the effects that network topologi cal features have on the collective dynamics, to understand how these systems can produce an effective collective response in the presence of changes in their environment, i.e., swarm intelligence. To investigate the influence of the network topology on the collective response, we consider the archetypal leader-follower linear consensus—a distributed deci sion-making model. Here, we find—through comparing various determinis tic graphs and an optimization framework—a nontrivial relationship between the frequency of the driving signal and the optimal network topology. As the pace of the leader increases, the optimal connectivity of the network, in terms of its degree, decreases monotonically. We further demonstrate this rich phe nomenology through the use of a swarm of land robots performing a nonlinear heading consensus. As a next step, we go beyond the effects of network degree and study the in tricate impact of network clustering and network distance. We find that the flow of information in the leader-follower linear consensus experiences a tran sition from simple contagion—i.e., based on pairwise interactions—to a com plex one—i.e., involving social influence and reinforcement when the pace of the leader increases. We uncover this rich phenomenology—so far limited to threshold-based decision-making processes—and show theoretically that it can be characterized as simple or complex by analyzing the correlations between specific network metrics and the performance of the collective behaviors—here measured as the collective frequency response. iv We also uncover the complex contagion in a swarm of land robots perform ing a nonlinear heading consensus. However, limitations with the number of agents led us to develop a large-scale internet-of-things testbed. This large-scale testbed allows us to more fully explore the richness found in the interplay be tween collective dynamics and network topology as well as tackle some of the challenges that arise in large networked systems. The results presented in this thesis greatly expand our understanding of the ef fects of network topology on collective dynamics. They have significant ramifi cations for our understanding of a range of social and animal group behaviors, as well as for the design of cooperative robot systems.