Spontaneous synchronization in large pendulum arrays

Experiments on mechanical oscillator arrays show that complete inphase synchronization can emerge in a matter of minutes, even for fairly large arrays started from random initial conditions. At the same time, one expects complete inphase synchronization to become increasingly difficult to observe as array size grows. We explore the conditions under which inphase synchronization prevails with the help of a simple, somewhat stylized, iterative map model which embodies the problem’s key dynamical features.