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Chimera states are dynamical patterns in networks of coupled oscillators inwhich regions of synchronous and asynchronous oscillation coexist. Althoughthese states are typically observed in large ensembles of oscillators andanalyzed in the continuum limit, chimeras may also occur in systems with finite(and small) numbers of oscillators. Focusing on networks of $2N$ phaseoscillators that are organized in two groups, we find that chimera states,corresponding to attracting periodic orbits, appear with as few as twooscillators per group and demonstrate that for $N>2$ the bifurcations thatcreate them are analogous to those observed in the continuum limit. Thesefindings suggest that chimeras, which bear striking similarities to dynamicalpatterns in nature, are observable and robust in small networks that arerelevant to a variety of real-world systems.

Chimera states in networks of phase oscillators: the case of two small populations