论文标题
在尺寸增强扰动下的嵌合体状态的瞬时寿命的缩放定律
Scaling law of transient lifetime of chimera states under dimension-augmenting perturbations
论文作者
论文摘要
二维相耦合振荡器的经典库拉莫托系统中产生的嵌合体状态是瞬态的，但它们是“长”瞬态，从某种意义上说，平均瞬时寿命随系统大小而成倍增长。对于相当大的系统，例如，由数百个振荡器组成的系统，在数值上计算或实验测量平均寿命是不可行的，因此嵌合体状态实际上是永久的。我们发现，在第三维中的小扰动使系统“略微”三维，将大大降低瞬时寿命。特别是，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，因为它仅以对数的范围来缩放。从物理上讲，这意味着在许多数量级上的扰动强度的降低，只要它不是零，就只会导致寿命增加。嵌合体状态的脆弱类型引起了人们对它们在物理系统中的可观察性的担忧。
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.
