耦合振子大系统中的回声现象。
Echo phenomena in large systems of coupled oscillators.
作者信息
Ott Edward, Platig John H, Antonsen Thomas M, Girvan Michelle
机构信息
Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, Maryland 20742, USA.
出版信息
Chaos. 2008 Sep;18(3):037115. doi: 10.1063/1.2973816.
As exemplified by the Kuramoto model, large systems of coupled oscillators may undergo a transition to phase coherence with increasing coupling strength. It is shown that below the critical coupling strength for this transition such systems may be expected to exhibit "echo" phenomena: a stimulation by two successive pulses separated by a time interval tau leads to the spontaneous formation of response pulses at a time tau, 2 tau, 3 tau,..., after the second stimulus pulse. Analysis of this phenomenon, as well as illustrative numerical experiments, are presented. The theoretical significance and potential uses of echoes in such systems are discussed.
以Kuramoto模型为例，耦合振子的大型系统可能会随着耦合强度的增加而发生向相位相干的转变。结果表明，在这种转变的临界耦合强度以下，这样的系统可能会表现出“回声”现象：由时间间隔τ隔开的两个连续脉冲的刺激会导致在第二个刺激脉冲之后的时间τ、2τ、3τ……自发形成响应脉冲。本文给出了对这一现象的分析以及说明性的数值实验。讨论了此类系统中回声的理论意义和潜在用途。
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