PHASE REGULATION OF COUPLED OSCILLATORS AND CHAOS

The phase entrainment of coupled oscillators, often confused with frequency entrainment, was first described by Huygens in 1665 as the ”sympathy of clocks”. As it refers to the independence of the equilibrium phase difference from variations in initial conditions or the strength of the coupling, we refer to this phenomenon as phase locking. In the context of ensembles of coupled oscillators, it has many important applications. Recently, Vassalo Pereira has given a derivation of the sympathy of clocks based on Andronov’s model for the pendulum clock, showing that it is the ”tick-tock” of the escapements, rather than the swings of the pendula, which are responsible for the phase regulation. Here, we generalize Vassalo Pereira’s result to arbitrary coupled oscillators, to obtain a geometric theory of phase regulation due to pulsatile forces. The extension of this geometric theory to chaotic attractors is indicated as well …