On study of quasiharmonic oscillator with nonlinearity and saturation

The apparatus of the theory of differential equations is a very effective means for studying oscillatory processes in various branches of physics and technology. Naturally, the most accessible for investigation are oscillatory systems with low nonlinearity. Moreover, the study of systems close to a harmonic oscillator (quasi-harmonic oscillator) is still of particular interest. In this paper, we give an example of the study of a quasi-harmonic oscillator (with non-linearity with saturation) by the method of approximate point mappings. The question of its synchronization is reduced to solving the question of the existence of fixed points of a point mapping, in the construction of which the method of successive approximations is applied. The question of the local applicability of the results of an approximate study is discussed in the paper.