Cyclic Pursuit: Symmetry, Reduction and Nonlinear Dynamics

In this dissertation, we explore the use of pursuit interactions as a building block for collective behavior, primarily in the context of constant bearing (CB) cyclic pursuit. Pursuit phenomena are observed throughout the natural environment and also play an important role in technological contexts, such as missile-aircraft encounters and interactions between unmanned vehicles. While pursuit is typically regarded as adversarial, we demonstrate that pursuit interactions within a cyclic pursuit framework give rise to seemingly coordinated group maneuvers. We model a system of agents (e.g. birds, vehicles) as particles tracing out curves in the plane, and illustrate reduction to the shape space of relative positions and velocities. Introducing the CB pursuit strategy and associated pursuit law, we consider the case for which agent i pursues agent i+1 (modulo n) with the CB pursuit law. After deriving closed-loop cyclic pursuit dynamics, we demonstrate asymptotic convergence to an invariant submanifold (corresponding to each agent attaining the CB pursuit strategy), and proceed by analysis of the reduced dynamics restricted to the submanifold. For the general setting, we derive existence conditions for relative equilibria (circling and rectilinear) as well as for system trajectories which preserve the shape of the collective (up to similarity), which we refer to as pure shape equilibria. For two illustrative low-dimensional cases, we provide a more comprehensive analysis, deriving explicit trajectory solutions for the two-particle "mutual pursuit" case, and detailing the stability properties of three-particle relative equilibria and pure shape equilibria. For the three-particle case, we show that a particular choice of CB pursuit parameters gives rise to remarkable almost-periodic trajectories in the physical space. We also extend our study to consider CB pursuit in three dimensions, deriving a feedback law for executing the CB pursuit strategy, and providing a detailed analysis of the two-particle mutual pursuit case. We complete the work by considering evasive strategies to counter the motion camouflage (MC) pursuit law. After demonstrating that a stochastically steering evader is unable to thwart the MC pursuit strategy, we propose a (deterministic) feedback law for the evader and demonstrate the existence of circling equilibria for the closed-loop pursuer-evader dynamics.

Flooded with Information from Social Media: Effects of Disaster Information Source and Visuals on Viewers' Cognitive, Affective, and Behavioral Responses

While a variety of crisis types loom as real risks for organizations and communities, and the media landscape continues to evolve, research is needed to help explain and predict how people respond to various kinds of crisis and disaster information. For example, despite the rising prevalence of digital and mobile media centered on still and moving visuals, and stark increases in Americans’ use of visual-based platforms for seeking and sharing disaster information, relatively little is known about how the presence or absence of disaster visuals online might prompt or deter resilience-related feelings, thoughts, and/or behaviors. Yet, with such insights, governmental and other organizational entities as well as communities themselves may best help individuals and communities prepare for, cope with, and recover from adverse events. Thus, this work uses the theoretical lens of the social-mediated crisis communication model (SMCC) coupled with the limited capacity model of motivated mediated message processing (LC4MP) to explore effects of disaster information source and visuals on viewers’ resilience-related responses to an extreme flooding scenario. Results from two experiments are reported. First a preliminary 2 (disaster information source: organization/US National Weather Service vs. news media/USA Today) x 2 (disaster visuals: no visual podcast vs. moving visual video) factorial between-subjects online experiment with a convenience sample of university students probes effects of crisis source and visuals on a variety of cognitive, affective, and behavioral outcomes. A second between-subjects online experiment manipulating still and moving visual pace in online videos (no visual vs. still, slow-pace visual vs. still, medium-pace visual vs. still, fast-pace visual vs. moving, slow-pace visual vs. moving, medium-pace visual vs. moving, fast-pace visual) with a convenience sample recruited from Amazon’s Mechanical Turk (mTurk) similarly probes a variety of potentially resilience-related cognitive, affective, and behavioral outcomes. The role of biological sex as a quasi-experimental variable is also investigated in both studies. Various implications for community resilience and recommendations for risk and disaster communicators are explored. Implications for theory building and future research are also examined. Resulting modifications of the SMCC model (i.e., removing “message strategy” and adding the new category of “message content elements” under organizational considerations) are proposed.