Resonance Phenomenon in Classical Cepheids

To investigate resonance phenomenon in classical cepheids, the non-linear radial oscillation of stars is studied based on the assumption that the non-adiabatic perturbation is expressed in terms of van der Pol\u27s type damping. Two- and three-wave resonance in this system is applied to classical cepheids to describe their bump and double-mode behavior. The phase of bump and the depression of amplitude are explained for bump cepheids. The double-periodicity is shown by the enhancement of the third overtone in three-wave resonance. Non-linear effect on resonant period is also discussed briefly