Abstract:
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.
Keywords:quasiharmonic oscillator, nonlinearity saturation, small parameter, asymptotic research methods, point
mapping method.