The study of coupled oscillators began in 1656 with Huygens’ invention of the pendulum clock and his subsequent observation of the “sympathy of two clocks.” In the following short course we will begin with the study of a single Stuart–Landau oscillator. Such a model describes the behavior of a limit-cycle oscillator near a Hopf bifurcation. The famous Kuramoto model (1975) was derived from an ensemble of such oscillators. We will derive the Kuramoto model, and study its various asymptotic outcomes depending on the values of K and ω. Recent trends in Neuroscience involve utilizing both Stuart–Landau and Kuramoto-type oscillators for mesoscopic brain modeling. Further, taking inspiration from Biology, the Machine Learning community has begun utilizing such oscillators to train neural networks in order to ameliorate the so-called oversmoothing problem. We will finish the course studying several of these applications.
Tuesday 11/11, 8:30-10:30 Aula Alfa.
Friday 14/11, 10:30-12:30. Aula C
Friday 14/11, 13:30 -15:30 Aula I
Contact: Giacomo Albi (giacomo.albi@univr.it)
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