Conceptualizing Synchronization Phenomena and its Applications

Abstract: Abstract Synchronization phenomena is evident in a number of different processes, both natural and artificial. The present thesis aims to investigate such phenomena by looking at what the necessary parameters are for the modeling of such phenomena and what models that have been proposed. The phenomena as such is then applied in the treatment of synchronizing an audio-recording that is off-time to a metronome in 4/4 running at 120 bpm. The thesis introduces the notion of synchronization first and foremost and then gives background on what the necessary tools are for the scientific study of synchronization. The background given allows one to construct a mathematical framework for modeling synchronization and the thesis thus arrives at the Kuramoto Model. The Kuramoto model is applied in the treatment of the audio and metronome. With a coupling strength of K = 1 in the Kuramoto model, near-perfect synchrony is achieved immediately after just one iteration of the model with phase-coherence = 0:9999. Changing the coupling strength to K = 0:5, synchrony arises after 6 iterations of the model for which the process develops smoothly. Synchrony can be achieved for any coupling strength K for this particular problem as both audio and metronome run at an angular frequency ! = 2=s [2].