Emergent behavior in complicated systems: Tinnitus, smarticles, and metronomes
Jackson, Zachary Lawrence
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Patterns of behavior can arise in many body systems that are qualitatively different than that of the individual elements. In this dissertation, we explore emergent behaviors through three different projects. The first is a dynamical model for the inner ear that explores both the onset of tinnitus and the effects of coordinated reset therapy. This non-invasive therapy recently found promising results in a clinical trial. Our model extends an existing theory of individual outer hair cell dynamics to include their mutual interaction, and considers how sustained activity can inhibit the natural recovery exhibited by normal (healthy) individuals. The model is investigated through numerical simulations and shows behavior broadly similar to that reported in the clinical study. Next, we describe the motion of a collection of enclosed "smarticles'', small three-link robots which move their arms according to a predetermined gate. Experiments show when all internal smarticles are performing a periodic gate, an enclosing ring can translate, but does not have a preferred direction. When one smarticle is made inactive and in a straight configuration the collective drifts on average either towards or away from the inactive smarticle, depending on the mass of the enclosing ring. To better understand this biased motion we develop a collision model for the system and then extend that model to include short term correlations to account for fluctuations. Lastly, we identify a class of non-equilibrium systems whose behavior can be described statistically even if it is deterministic in principle. These systems are characterized by episodes of distinct behaviors with irregular transitions between them, and a preference for more ordered patterns of motion. We explore this behavior through a series of concrete examples.