When nonlinear oscillators are periodically driven, the possibility of resonance arises.

his figure demonstrates the phenomenon of resonance.  The two oscillators are identical and we represent them as pendula  Like all real pendula, they are subject to friction, which tends to damp out oscillations.  Further, they are being driven by a periodically-varying force.  The only difference between them was the position in which they started.  One oscillates with only a small amplitude, the other with a much larger amplitude but precisely the same period.  We say that the second oscillator resonates with the driving force, to produce a large amplitude oscillation.

A consequence of including seasonality in the predator-prey models we have discussed is to create resonant solutions.  These large-amplitude, long-period solutions resemble the cycles of boreal mammal populations.