Two non-linear oscillators will synchronize when weakly linked.

he animation above demonstrates the phenomenon of phase-locking or entrainment.  At the left-hand side of the equation are two uncoupled oscillators.  They are not identical: the first has a shorter period than the second.  Although they start out in the same place, they rapidly fall out of phase.

At the right-hand side of the equation, the same two oscillators have been weakly coupled.  After the brief time it takes for the transient behavior to die out, the oscillators are synchronized.  One oscillator has a constant phase lag with respect to the other.

The phenomenon is quite general.  It applies, at least in principle, to nonlinear oscillators, whether these are found in mechanical clocks, electrical circuits, female ovulation cycles, or predator-prey oscillations.  Could this phenomenon be responsible for the observed synchrony of snowshoe hare cycles across wide regions of the North American continent?