A note on the generalized Rayleigh equation: limit cycles and stability

The aim of the present paper is to give an analytical proof on the existence and stability of the limit cycles in the generalized Rayleigh equation, which models diabetic chemical processes through a constant area duct where the effect of heat addition or rejection is considered, ${\frac{d^{2}x}{dt^{2}}+x = \varepsilon(1-(\frac{dx}{dt}) ^{2n})\,\frac{dx}{dt}}$ where n is a positive integer and ε a small real parameter. The main tool used for it is the averaging theory.