排斥作用下的最小嵌合体
Smallest chimeras under repulsive interactions
摘要：
我们提出了一个示范性的系统，三个相同的振荡器在一个环相互排斥，显示嵌合体模式。单个振荡器的动力学由超导约瑟夫森结控制。令人惊讶的是，排斥的相互作用建立了一个对称的完全同步的环，这是打破了越来越多的相互作用时，通过一系列的异步状态（周期和混沌），但最终出现嵌合体状态。嵌合体模式出现在混沌旋转运动的三个路口时，两个路口的发展连贯，而第三个路口是不连贯的。对于较大的排斥耦合，结演变成另一个嵌合体模式在一个周期性的状态时，两个结保持一致的旋转运动和一个过渡到不相干的librational运动。这种嵌合体模式是敏感的初始条件，在这个意义上说，嵌合体状态翻转到另一种模式时，两个结切换到连贯的librational运动和第三个结仍然在旋转运动，但不连贯。嵌合体的模式被检测到通过使用部分和整体的错误功能的连接，而librational和旋转运动被确定的天平动指数。所有的集体状态，完全同步，去同步化和两个嵌合体模式，被描绘在一个参数平面的路口环，其中完全同步的边界是由使用主稳定性函数划定。
英文摘要：
We present an exemplary system of three identical oscillators in a ring interacting repulsively to show up chimera patterns. The dynamics of individual oscillators is governed by the superconducting Josephson junction. Surprisingly, the repulsive interactions establish a symmetry of compelete synchrony in the ring, which is broken with increasing interactions when the junctions pass through serials of asynchronous states (periodic and chaotic), but finally emerge into chimera states. The chimera pattern appears in chaotic rotational motion of the three junctions when two junctions evolve coherently while the third junction is incoherent. For larger repulsive coupling, the junctions evolves into another chimera pattern in a periodic state when two junctions remain coherent in rotational motion and one transits to incoherent librational motion. This chimera pattern is sensitive to initial conditions, in the sense, that the chimera state flips to another pattern when two junctions switch to coherent librational motion and the third junction remains in rotational motion, but incoherent. The chimera patterns are detected by using partial and global error functions of the junctions while the librational and rotational motions are identified by a libration index. All the collective states, complete synchrony, desynchronization and two chimera patterns, are delineated in a parameter plane of the ring of junctions, where the boundaries of complete synchrony are demarcated by using the master stability function.
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