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| Networks of coupled oscillators have been studied extensively because of their wide applications in physics, chemistry, and biology. When the coupling is weak, phase reduction leads to a simplified description of the dynamics. Among the phase-coupled models that result, Kuramoto-type models are best known. Numerous studies with either local or global coupling have been made, but the role of nonlocal coupling remains poorly understood. In 2002 Kuramoto and Battogtokh [{\it Nonlinear Phenom. Complex Syst.} {\bf 5} 380--385 (2002)] investigated a system of identical phase-coupled oscillators with a nonlocal coupling and found a solution consisting of coherent, phased-locked oscillators embedded in a background state of incoherent oscillators, later referred to as a chimera state [D.M. Abrams and S.H. Strogatz, {\it Phys. Rev. Lett.} {\bf 93} 174102 (2004)]. These states usually coexist with a stable fully synchronized state and are therefore hard to find. Here, we propose a nonlocal phase-coupled model in which chimera states can be found easily. By adjusting the parameters of the model, the number of coherent clusters can be controled. Stability properties and bifurcations of these states are described, with particular emphasis on the appearance of a traveling chimera state. |
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