The weak nonlinearity and the long time scale of the amplitude variation allows the temporal description of the pulsating system to be simplified to that of only the pulsation amplitudes, thus eliminating motion on the short time scale of the period. The result is a description of the system in terms of amplitude equations that are truncated to low powers of the amplitudes. Such amplitude equations have been derived by a variety of techniques, e.g. the Poincaré–Lindstedt method of elimination of secular terms, or the multi-time asymptotic perturbation method, and more generally, normal form theory.