Abstract:
The article considers the possibility of investigating the synchronization of a quasiharmonic oscillator with nonlinearity of
the type of a cubic parabola by the method of approximate point mappings. The synchronization of a quasiharmonic oscillator
comes to solving the problem of the existence of fixed points on a point map, while the method of successive approximations
is applied for their construction. The proposed method of investigation is an asymptotic method; therefore, the applicability of
the results of an approximate investigation at specific values of the small parameter is also important. In this paper, we propose
to consider the problem of applicability of the results of an approximate investigation, estimating the degree of closeness of the
approximate point mapping to the exact mapping.
Keywords:quasiharmonic oscillator, small parameter, asymptotic methods of investigation, method of point mappings.