title: Chimera states in networks of phase oscillators: The case of two small populations.
abstract: Chimera states are dynamical patterns in networks of coupled oscillators in which regions of synchronous and asynchronous oscillation coexist. Although these states are typically observed in large ensembles of oscillators and analyzed in the continuum limit, chimeras may also occur in systems with finite (and small) numbers of oscillators. Focusing on networks of 2N phase oscillators that are organized in two groups, we find that chimera states, corresponding to attracting periodic orbits, appear with as few as two oscillators per group and demonstrate that for N>2 the bifurcations that create them are analogous to those observed in the continuum limit. These findings suggest that chimeras, which bear striking similarities to dynamical patterns in nature, are observable and robust in small networks that are relevant to a variety of real-world systems.
authors: Mathematics Department, Rose-Hulman Institute of Technology, Terre Haute, Indiana 47803, USA.
authors: Mark J
authors: MJ
authors: Panaggio
authors: Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, Illinois 60208, USA.|Department of Physics and Astronomy, Northwestern University, Evanston, Illinois 60208, USA.|Northwestern Institute on Complex Systems, Northwestern University, Evanston, Illinois 60208, USA.
authors: Daniel M
authors: DM
authors: Abrams
authors: Centre for Systems, Dynamics and Control, Harrison Building, Exeter EX4 4QF, United Kingdom.
authors: Peter
authors: P
authors: Ashwin
authors: Institute of Natural and Mathematical Sciences, Massey University, Private Bag 102-904 NSMC, Auckland, New Zealand.
authors: Carlo R
authors: CR
authors: Laing