Abstract
Coupled linear oscillators provide a central paradigm for the combined behavior of coupled systems and the emergence of normal modes. Nonlinear coupling of two autonomous oscillators provides an equally important paradigm for the emergence of collective behavior through synchronization. Simple asymmetric coupling of integrate and fire oscillators captures the essence of frequency locking. Quasiperiodicity on the torus (action-angle oscillators) with nonlinear coupling demonstrates phase locking, while the sine-circle map is a discrete map that displays multiple Arnold tongues at frequency-locking resonances. External synchronization of a phase oscillator is analyzed in terms of the “slow” phase difference, resulting in a beat frequency and frequency entrainment that are functions of the coupling strength.
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