On investigation of forced synchronization by the method of approximated point mappings

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.