interesting behavior can result from varying the amplitude and frequency of the external voltage. for instance, the oscillator may produce an oscillating voltage whose frequency is a submultiple of the external frequency. this phenomenon is known as "submultiplication" or "demultiplication", and was first observed in 1927 by balthasar van der pol and his collaborator jan van der mark. in some cases the ratio of the external frequency to the frequency of the oscillation observed in the circuit may be a rational number, or even an irrational one (the latter case is known as the "quasiperiodic" regime). when the periodic and quasiperiodic regimes overlap, the behavior of the circuit may become aperiodic, meaning that the pattern of the oscillations never repeats. this aperiodicity correspond to the behavior of the circuit becoming "chaotic" (see chaos theory).