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Instability in the form of growing oscillations (overstahility) can occur iii convectively unstable fluids which rotate, have magnetic fields, or are compressible, so long as thermal dissipation operates. To clarify the manner in which thermal dissipation causes instability, a model oscillator which exhibits overstability is constructed. The governing equations are derived and the linear stability is discussed. The non4inear behavior of the oscillator is then investigated. The governing non4inear equation is third order in time, and it therefore is a simple representative example of the type of equation which describes non-linear stellar pulsations. The equation contains two parameters, and a great variety of solutions is found, depending on the values taken. One kind of solution shows relaxation oscillations with superposed variations, while, in a particular range of the governing parameters, the numerical solutions of the governing equation are aperiodic or irregular. A mathematical explanation of this irregularity is suggested, and the possibility that it might be relevant to irregular variability in stars is raised. The general conclusion is suggested that a great variety of oscillatory phenomena, analogous to several of those observed in variable stars, can be generated from a single instability mechanism, provided the essential non4inearities are retained and the law of dissipation is appropriately chosen.
Moore et al. (Tue,) studied this question.