Coupled Oscillators and Quasiperiodicity - Dynamical Systems Extra Credit | Lecture 9

In this lecture we turn to another setting for planar dynamical systems given by flows on the torus. In particular, we will study the Kuramoto model of two coupled oscillators, each having phase space on the circle. In the uncoupled system we show that there are two distinct cases for the flow of the system, differentiated by whether the intrinsic frequencies of the coupled oscillators are rationally related or not. The latter case leads to quasiperiodicity wherein trajectories wind densely around the torus. We then use this knowledge to examine the coupled system, showing that a saddle-node bifurcation leads to phase-locking.

Recall the basics of flows on the circle:    • Flows on the Circle - Dynamical Systems | ...  

Modelling fireflies with coupled oscillators:    • Modelling Firefly Entrainment - Dynamical ...  

Lecture series on dynamical systems:    • Welcome - Dynamical Systems | Intro Lecture  

Lectures series on differential equations:    • Welcome - Ordinary Differential Equations ...  

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