In contrast, the irregularity of the large amplitude Population II stars is more challenging to explain. The variation of the pulsation amplitude over one period implies large dissipation, and therefore there exists no center manifold. Various mechanisms have been proposed, but are found lacking. One, suggests the presence of several closely spaced pulsation frequencies that would beat against each other, but no such frequencies exist in the appropriate stellar models. Another, more interesting suggestion is that the variations are of a stochastic nature, but no mechanism has been proposed or exists that could provide the energy for such large observed amplitude variations. It is now established that the mechanism behind the irregular light curves is an underlying low dimensional chaotic dynamics (see also Chaos theory). This conclusion is based on two types of studies.