Echo phenomena in large systems of coupled oscillators Available to Purchase

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 $τ$ leads to the spontaneous formation of response pulses at a time $τ,2τ,3τ,…$⁠, 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.