Stellar pulsations are caused by expansions and contractions in the outer layers as a star seeks to maintain equilibrium. These fluctuations in stellar radius cause corresponding changes in the luminosity of the star. Astronomers are able to deduce this mechanism by measuring the spectrum and observing the Doppler effect. Many intrinsic variable stars that pulsate with large amplitudes, such as the classical Cepheids, RR Lyrae stars and large-amplitude Delta Scuti stars show regular light curves.

This regular behavior is in contrast with the variability of stars that lie parallel to and to the high-luminosity/low-temperature side of the classical variable stars in the Hertzsprung–Russell diagram. These giant stars are observed to undergo pulsations ranging from weak irregularity, when one can still define an average cycling time or period, (as in most RV Tauri and semiregular variables) to the near absence of repetitiveness in the irregular variables. The W Virginis variables are at the interface; the short period ones are regular and the longer period ones show first relatively regular alternations in the pulsations cycles, followed by the onset of mild irregularity as in the RV Tauri stars into which they gradually morph as their periods get longer. Stellar evolution and pulsation theories suggest that these irregular stars have a much higher luminosity to mass (L/M) ratios.

Many stars are non-radial pulsators, which have smaller fluctuations in brightness than those of regular variables used as standard candles.

A prerequisite for irregular variability is that the star be able to change its amplitude on the time scale of a period. In other words, the coupling between pulsation and heat flow must be sufficiently large to allow such changes. This coupling is measured by the relative linear growth- or decay rate κ (kappa) of the amplitude of a given normal mode in one pulsation cycle (period). For the regular variables (Cepheids, RR Lyrae, etc.) numerical stellar modeling and linear stability analysis show that κ is at most of the order of a couple of percent for the relevant, excited pulsation modes. On the other hand, the same type of analysis shows that for the high L/M models κ is considerably larger (30% or higher).

For the regular variables the small relative growth rates κ imply that there are two distinct time scales, namely the period of oscillation and the longer time associated with the amplitude variation. Mathematically speaking, the dynamics has a center manifold, or more precisely a near center manifold. In addition, it has been found that the stellar pulsations are only weakly nonlinear in the sense that their description can be limited powers of the pulsation amplitudes. These two properties are very general and occur for oscillatory systems in many other fields such as population dynamics, oceanography, plasma physics, etc.

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.

For example, in the case of two non-resonant modes, a situation generally encountered in RR Lyrae variables, the temporal evolution of the amplitudes A₁ and A₂ of the two normal modes 1 and 2 is governed by the following set of ordinary differential equations $${\displaystyle {\begin{aligned}{\frac {dA_{1}}{dt}}&=\kappa _{1}A_{1}+\left(Q_{11}A_{1}^{2}+Q_{12}A_{2}^{2}\right)A_{1}\\[1ex]{\frac {dA_{2}}{dt}}&=\kappa _{2}A_{2}+\left(Q_{21}A_{1}^{2}+Q_{22}A_{2}^{2}\right)A_{2}\end{aligned}}}$$ where the Q_ij are the nonresonant coupling coefficients.

These amplitude equations have been limited to the lowest order nontrivial nonlinearities. The solutions of interest in stellar pulsation theory are the asymptotic solutions (as time tends towards infinity) because the time scale for the amplitude variations is generally very short compared to the evolution time scale of the star which is the nuclear burning time scale. The equations above have fixed point solutions with constant amplitudes, corresponding to single-mode (A₁${\displaystyle \neq }$ 0, A₂ = 0) or (A₁ = 0, A₂${\displaystyle \neq }$ 0) and double-mode (A₁${\displaystyle \neq }$ 0, A₂${\displaystyle \neq }$0) solutions. These correspond to singly periodic and doubly periodic pulsations of the star. No other asymptotic solution of the above equations exists for physical (i.e., negative) coupling coefficients.