2017/07/31 by Jordan Snyder, Anatoly Zlotnik, Aric Hagberg
Computer Science · Engineering · Mathematics · Neuroscience · Physics and Astronomy · #Acoustics #Computer science #Control theory (sociology) #Coupling (piping) #Engineering #Entrainment (biomusicology) #Mathematics #Neural dynamics and brain function #Nonlinear Dynamics and Pattern Formation #Offset (computer science) #Physics #Rhythm #SIGNAL (programming language) #Slime Mold and Myxomycetes Research #Stability (learning theory) #Synchronization (alternating current) #Topology (electrical circuits) #nlin.AO
paper · pdf · doi:10.1063/1.4994567
arxiv created 2017/09/22 · openalex publication_date 2017/10/01 · arxiv updated 2017/10/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Complex natural and engineered systems are ubiquitous, and their behavior is challenging to characterize and control. We examine the design of the entrainment process for an uncountably infinite collection of coupled phase oscillators that are all subject to the same periodic driving signal. In the absence of coupling, an appropriately designed input can result in each oscillator attaining the frequency of the driving signal, with a phase offset determined by its natural frequency. We consider a special case of interacting oscillators in which the coupling tends to destabilize the phase configuration to which the driving signal would send the collection in the absence of coupling. In this setting, we derive stability results that characterize the trade-off between the effects of driving and coupling, and compare these results to the well-known Kuramoto model of a collection of free-running coupled oscillators.