Chimera States in a Ring of Nonlocally Coupled Oscillators (arXiv) Export

@article{citeulike:5784763, abstract = {Arrays of identical limit-cycle oscillators have been used to model a widevariety of pattern-forming systems, such as neural networks, convecting fluids,laser arrays, and coupled biochemical oscillators. These systems are known toexhibit rich collective behavior, from synchrony and traveling waves tospatiotemporal chaos and incoherence. Recently, Kuramoto and his colleaguesreported a strange new mode of organization--here called the chimera state--inwhich coherence and incoherence exist side by side in the same system ofoscillators. Such states have never been seen in systems with either local orglobal coupling; they are apparently peculiar to the intermediate case ofnonlocal coupling. Here we give an exact solution for the chimera state, for aone-dimensional ring of phase oscillators coupled nonlocally by a cosinekernel. The analysis reveals that the chimera is born in a continuousbifurcation from a spatially modulated drift state, and dies in a saddle-nodecollision with an unstable version of itself.}, archivePrefix = {arXiv}, author = {Abrams, Daniel M. and Strogatz, Steven H.}, citeulike-article-id = {5784763}, citeulike-linkout-0 = {http://arxiv.org/abs/nlin.PS/0504046}, citeulike-linkout-1 = {http://arxiv.org/pdf/nlin.PS/0504046}, day = {11}, eprint = {nlin.PS/0504046}, keywords = {chimera, sync}, month = {May}, posted-at = {2009-09-14 23:03:49}, priority = {2}, title = {Chimera States in a Ring of Nonlocally Coupled Oscillators (arXiv)}, url = {http://arxiv.org/abs/nlin.PS/0504046}, year = {2006} }

TY - JOUR ID - citeulike:5784763 L3 - citeulike-article-id:5784763 N2 - Arrays of identical limit-cycle oscillators have been used to model a widevariety of pattern-forming systems, such as neural networks, convecting fluids,laser arrays, and coupled biochemical oscillators. These systems are known toexhibit rich collective behavior, from synchrony and traveling waves tospatiotemporal chaos and incoherence. Recently, Kuramoto and his colleaguesreported a strange new mode of organization--here called the chimera state--inwhich coherence and incoherence exist side by side in the same system ofoscillators. Such states have never been seen in systems with either local orglobal coupling; they are apparently peculiar to the intermediate case ofnonlocal coupling. Here we give an exact solution for the chimera state, for aone-dimensional ring of phase oscillators coupled nonlocally by a cosinekernel. The analysis reveals that the chimera is born in a continuousbifurcation from a spatially modulated drift state, and dies in a saddle-nodecollision with an unstable version of itself. TI - Chimera States in a Ring of Nonlocally Coupled Oscillators (arXiv) KW - chimera KW - sync AU - Abrams, Daniel AU - Strogatz, Steven PY - 2006/May/11/ UR - http://arxiv.org/abs/nlin.PS/0504046 ER -