  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.
