Vibration that Accord and Mob

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Synchronization occurs in many natural and technological systems, from cardiac pacemaker cells to coupled lasers. In the synchronized state, the individual cells or lasers coordinate the timing of their oscillations, but they do not move through space. A complementary form of self-organization occurs among swarming insects, flocking birds, or schooling fish; now the individuals move through space, but without conspicuously altering their internal states. Here we explore systems in which both synchronization and swarming occur together. Specifically, we consider oscillators whose phase dynamics and spatial dynamics are coupled. We call them swarmalators, to highlight their dual character. A case study of a generalized Kuramoto model predicts five collective states as possible long-term modes of organization. These states may be observable in groups of sperm, Japanese tree frogs, colloidal suspensions of magnetic particles, and other biological and physical systems in which self-assembly and synchronization interact.
Studies of swarming and synchronization have much in common. Both involve large, self-organizing groups of individuals interacting according to simple rules. Both lie at the intersection of nonlinear dynamics and statistical physics. Nevertheless the two fields have, by and large, remained disconnected. Studies of swarms focus on how animals move, while neglecting the dynamics of their internal states. Studies of synchronization do the opposite: they focus on oscillators’ internal dynamics, not on their motion. We propose a simple model of a swarmalators system which lets us study some of its collective states analytically. We hope our work will draw attention to this class of problems, and stimulate the discovery and characterization of natural and technological systems of swarmalators.
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