It is convenient to consider four distinct dynamical
regimes whose different characteristics arise from differences in the amount of interaction between particles and the degree of
damping in the system (Fig. ). These
four dynamical regimes are interesting with regard to their proposed universality. According to Blümel, although the quantitative boundaries between these four regimes vary as a function of the Mathieu parameters a and q, the existence and qualitative nature of the four dynamical
regimes persist throughout the range of experimentally-explored Mathieu parameters, right up to the Mathieu instability (MI), at which point the classifications are immaterial since particle motions are unbounded. Moreover, Blümel asserts that the qualitative description of the four dynamical regimes is manifest in a variety of systems, including a collection of Paul-trapped particles interacting via the screened Yukawa potential, a periodically perturbed hydrogen atom or polar molecule, and a hydrogen atom in a strong magnetic field.