耦合 Adler 型振荡器的复杂性与向混沌的转变
Complexity and transition to chaos in coupled Adler-type oscillators
AI总结：
本文研究了具有最近邻耦合的 Adler 型振荡器在参数空间针状区域内的动力学行为，发现其内部存在平滑的动力学变化与异质性，并在混沌起始时局部形成具有无序边界的相干振荡器集群。
摘要：
耦合非线性振荡器在动力学研究中无处不在。大量的行为主要是在全局耦合系统中发现的。从复杂性的角度来看，局部耦合系统研究较少，这正是本文的主题。由于假设弱耦合，因此使用了相位近似。特别地，仔细刻画了具有最近邻耦合的 Adler 型振荡器在参数空间中所谓的针状区域。强调这一区域的原因是，在它与周围混沌区域的边界处，已有研究报道了在混沌边缘的计算增强。本研究表明，在针状区域内可以发现不同的行为，并且能够识别出动力学的平滑变化。熵测度进一步突显了该区域的异质性及其有趣特征，正如在时空图中所见。时空图中波状模式的出现指向了两个维度上的非平凡相关性。随着控制参数的变化，波模式发生改变但并未超出针状区域。空间相关性仅在混沌起始时局部实现，不同的振荡器集群表现出相干行为，而它们之间出现无序边界。
英文摘要：
Coupled non-linear oscillators are ubiquitous in dynamical studies. A wealth of behaviors have been found mostly for globally coupled systems. From a complexity perspective, less studied have been systems with local coupling, which is the subject of this contribution. The phase approximation is used, as weak coupling is assumed. In particular, the so called needle region, in parameter space, for Adler-type oscillators with nearest neighbors coupling is carefully characterized. The reason for this emphasis is that in the border of this region to the surrounding chaotic one, computation enhancement at the edge of chaos has been reported. The present study shows that different behaviors within the needle region can be found, and a smooth change of dynamics could be identified. Entropic measures further emphasize the region's heterogeneous nature with interesting features, as seen in the spatiotemporal diagrams. The occurrence of wave-like patterns in the spatiotemporal diagrams points to non-trivial correlations in both dimensions. The wave patterns change as the control parameters change without exiting the needle region. Spatial correlation is only achieved locally at the onset of chaos, with different clusters of oscillators behaving coherently while disordered boundaries appear between them.
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