增维微扰下嵌合态瞬态寿命的标度律
Scaling law of transient lifetime of chimera states under dimension-augmenting perturbations
摘要：
在经典的仓本二维相位耦合振荡器系统中产生的嵌合态是瞬态的，但它们是“长”瞬态，在这个意义上，平均瞬态寿命随系统大小呈指数增长。对于相当大的系统，例如，对于那些由几百个振荡器组成的系统，不可能用数值计算或实验测量平均寿命，因此嵌合态实际上是永久的。我们发现，在第三个维度的小扰动，使系统的“轻微”三维，将显着减少瞬态寿命。特别地，在这样的扰动下，实际上无限的平均瞬态寿命将变得非常短，因为它仅与扰动的幅度成比例。物理上，这意味着微扰强度在许多数量级上的减小，只要它不为零，将导致寿命的增量增加。嵌合体状态的脆弱性引起了人们对它们在物理系统中的可观察性的关注。
英文摘要：
Chimera states arising in the classic Kuramoto system of two-dimensional phase coupled oscillators are transient but they are "long" transients in the sense that the average transient lifetime grows exponentially with the system size. For reasonably large systems, e.g., those consisting of a few hundreds oscillators, it is infeasible to numerically calculate or experimentally measure the average lifetime, so the chimera states are practically permanent. We find that small perturbations in the third dimension, which make system "slightly" three-dimensional, will reduce dramatically the transient lifetime. In particular, under such a perturbation, the practically infinite average transient lifetime will become extremely short, because it scales with the magnitude of the perturbation only logarithmically. Physically, this means that a reduction in the perturbation strength over many orders of magnitude, insofar as it is not zero, would result in only an incremental increase in the lifetime. The uncovered type of fragility of chimera states raises concerns about their observability in physical systems.
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