Transient processes in the harmonic synchronization of self-excited oscillators. I

Detinko, V. N.; Merzlyakova, M. N.; Babenko, S. V.

doi:10.1007/bf00891469

Cited by 1 publication

(1 citation statement)

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“…Therefore, similar features observed in our results might be expected in other synchronization scenarios (see Supporting Information S1 ). The time to synchronization for a network of oscillators has been studied for several systems using analytical approaches [36] – [40] and numerical simulations [41] – [43] . Most synchronization studies focused on specific model oscillators at the network level and derived scaling laws associated with the number of oscillators.…”

Section: Discussionmentioning

confidence: 99%

How to Achieve Fast Entrainment? The Timescale to Synchronization

Granada

Herzel

2009

PLoS ONE

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Entrainment, where oscillators synchronize to an external signal, is ubiquitous in nature. The transient time leading to entrainment plays a major role in many biological processes. Our goal is to unveil the specific dynamics that leads to fast entrainment. By studying a generic model, we characterize the transient time to entrainment and show how it is governed by two basic properties of an oscillator: the radial relaxation time and the phase velocity distribution around the limit cycle. Those two basic properties are inherent in every oscillator. This concept can be applied to many biological systems to predict the average transient time to entrainment or to infer properties of the underlying oscillator from the observed transients. We found that both a sinusoidal oscillator with fast radial relaxation and a spike-like oscillator with slow radial relaxation give rise to fast entrainment. As an example, we discuss the jet-lag experiments in the mammalian circadian pacemaker.

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