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Entrainment of Coupled Oscillators

Student-Run Applied & Math Seminar

Speaker: Jordan Snyder, UCD Math
Location: 2112 MSB
Start time: Wed, Oct 12 2016, 12:10PM

Complex systems are ubiquitous, and often difficult to control. As a toy model for the control of a complex system, we take a system of coupled phase oscillators, all subject to the same periodic driving signal. It was shown by Anatoly Zlotnik and collaborators that in the absence of coupling, this can result in each oscillator attaining the frequency of the driving signal, with a phase offset determined by the oscillator's natural frequency. We consider a special case in which the coupling tends to destabilize the phase configuration to which the driving signal would send the oscillators in the absence of coupling. In this setting we derive stability estimates that capture the trade-off between driving and coupling, and compare these results to the unforced version (i.e. the standard Kuramoto model).