Application of He's method to the modified Rayleigh equation

In this work we analyze the application of He’s variational method for an estimation of limit cycles and oscillation periods for the class of self-sustained oscillations described by the modified Rayleigh equation. The main goal of the research is to find suitable trial functions which allow to reproduce the period of limit-cycle motion with a high degree of accuracy. There is an especial consideration of the Selkov model in the modified Rayleigh form having only one extremum that does not allow to apply the classical method of slow and fast motions. In this case He’s method allows to find the period of a limit-cycle motion with a high accuracy and to predict its value for various parameters of the concerned equations. Thus, it is possible to assert that at a correct choice of trial function the considered method gives exact results not only in the case of harmonic oscillations but also in the case of relaxation ones.