Chimera states in a ring of nonlocally coupled oscillators
Chimera states in a ring of nonlocally coupled oscillators
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DOI：
10.1142/s0218127406014551
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发表时间：
2006-01-01
影响因子：
2.2
通讯作者：
Strogatz, SH
中科院分区：
文献类型：
--
作者：
Abrams, DM;Strogatz, SH
相同的极限环振荡器的阵列已被用来模拟各种各样的模式形成系统，如神经网络，对流流体，激光阵列和耦合生化振荡器。已知这些系统表现出丰富的集体行为，从同步和行波到时空混沌和不相干。最近，仓本和他的同事报道了一种奇怪的新组织模式--这里称为嵌合体状态--在这种状态下，相干和非相干并存于同一个振荡器系统中。这种状态在具有局部或全局耦合的系统中从未见过;它们显然是非局部耦合的中间情况所特有的。在这里，我们给出了一个精确的解决方案的嵌合状态，一维环的相位振荡器耦合非局部的余弦核。分析表明，嵌合体出生在一个连续的分歧从空间调制的漂移状态，并死在鞍结碰撞与不稳定的版本本身。
Arrays of identical limit-cycle oscillators have been used to model a wide variety of pattern-forming systems, such as neural networks, convecting fluids, laser arrays and coupled biochemical oscillators. These systems are known to exhibit rich collective behavior, from synchrony and traveling waves to spatiotemporal chaos and incoherence. Recently, Kuramoto and his colleagues reported a strange new mode of organization-here called the chimera state-in which coherence and incoherence exist side by side in the same system of oscillators. Such states have never been seen in systems with either local or global coupling; they are apparently peculiar to the intermediate case of nonlocal coupling. Here we give an exact solution for the chimera state, for a one-dimensional ring of phase oscillators coupled nonlocally by a cosine kernel. The analysis reveals that the chimera is born in a continuous bifurcation from a spatially modulated drift state, and dies in a saddle-node collision with an unstable version of itself.