A class of underwater vehicles are modelled as Newtonian particles for navigation and control. We show a general method that controls cooperative Newtonian particles to generate patterns on closed smooth curves. These patterns are chosen for good sampling performance using mobile sensor networks. We measure the spacing between neighbouring particles by the relative curve phase along the curve. The distance between a particle and the desired curve is measured using an orbit function. The orbit value and the relative curve phase are then used as feedback to control motion of each particle. From an arbitrary initial configuration, the particles converge asymptotically to form an invariant pattern on the desired curves. We describe application of this method to control underwater gliders in a field experiment in Buzzards Bay, MA in March 2006.

We propose a continuous-time multi-option nonlin-ear generalization of classical linear weighted-average opinion dynamics. Nonlinearity is introduced by saturating opinion exchanges, and this is enough to enable a significantly greater range of opinion-forming behaviors with our model as compared to existing linear and nonlinear models. For a group of agents that communicate opinions over a network, these behaviors include multistable agreement and disagreement, tunable sensitivity to input, robustness to disturbance, flexible transition between patterns of opinions, and opinion cascades. We derive network-dependent tuning rules to robustly control the system behavior and we design state-feedback dynamics for the model parameters to make the behavior adaptive to changing external conditions. The model provides new means for systematic study of dynamics on natural and engineered networks, from information spread and political polarization to collective decision making and dynamic task allocation.

Flocks of starlings exhibit a remarkable ability to maintain cohesion as a group in highly uncertain environments and with limited, noisy information. Recent work demonstrated that individual starlings within large flocks respond to a fixed number of nearest neighbors, but until now it was not understood why this number is seven. We analyze robustness to uncertainty of consensus in empirical data from multiple starling flocks and show that the flock interaction networks with six or seven neighbors optimize the trade-off between group cohesion and individual effort. We can distinguish these numbers of neighbors from fewer or greater numbers using our systems-theoretic approach to measuring robustness of interaction networks as a function of the network structure, i.e., who is sensing whom. The metric quantifies the disagreement within the network due to disturbances and noise during consensus behavior and can be evaluated over a parameterized family of hypothesized sensing strategies (here the parameter is number of neighbors). We use this approach to further show that for the range of flocks studied the optimal number of neighbors does not depend on the number of birds within a flock; rather, it depends on the shape, notably the thickness, of the flock. The results suggest that robustness to uncertainty may have been a factor in the evolution of flocking for starlings. More generally, our results elucidate the role of the interaction network on uncertainty management in collective behavior, and motivate the application of our approach to other biological networks. Starling flocks move in beautiful ways that both captivate and intrigue the observer. Previous work has shown that starlings pay attention to their seven closest neighbors, but until now it was not understood why this number is seven. Our paper explains the mystery: when uncertainty in sensing is present, interacting with six or seven neighbors optimizes the balance between group cohesiveness and individual effort. To prove this result we develop a new systems-theoretic approach for understanding noisy consensus dynamics. The approach allows the evaluation of robustness over a family of hypothesized sensing strategies using observations of the spatial positions of birds within the flock. We apply this approach to experimental data from wild starling flocks, and find that six or seven neighbors yield maximal robustness. The implication that robustness of cohesion may have been a factor in the evolution of flocking has significant consequences for evolutionary biology. In addition, the results and the versatility of the approach have implications for uncertainty management in social and technological networks.

Significance: Political polarization threatens democracy in America. This article helps illuminate what drives it, as well as what factors account for its asymmetric nature. In particular, we focus on positive feedback among members of Congress as the key mechanism of polarization. We show how public opinion, which responds to the laws legislators make, in turn drives the feedback dynamics of political elites. Specifically, we find that voters’ “policy mood,” i.e., whether public opinion leans in a more liberal or conservative direction, drives asymmetries in elite polarization over time. Our model also demonstrates that once self-reinforcing processes among elites reach a critical threshold, polarization rapidly accelerates. By tying together elite and voter dynamics, this paper presents a unified theory of political polarization.

Previously, we showed using a computational agent-based model that a group of animals moving together can make a collective decision on direction of motion, even if there is a conflict between the directional preferences of two small subgroups of “informed” individuals and the remaining “uninformed” individuals have no directional preference. The model requires no explicit signaling or identification of informed individuals; individuals merely adjust their steering in response to socially acquired information on relative motion of neighbors. In this paper, we show how the dynamics of this system can be modeled analytically, and we derive a testable result that adding uninformed individuals improves stability of collective decision making. We first present a continuous-time dynamic model and prove a necessary and sufficient condition for stable convergence to a collective decision in this model. The stability of the decision, which corresponds to most of the group moving in one of two alternative preferred directions, depends explicitly on the magnitude of the difference in preferred directions; for a difference above a threshold the decision is stable and below that same threshold the decision is unstable. Given qualitative agreement with the results of the previous simulation study, we proceed to explore analytically the subtle but important role of the uninformed individuals in the continuous-time model. Significantly, we show that the likelihood of a collective decision increases with increasing numbers of uninformed individuals.