On the effect of nonlinearity types on the results of studying the synchronization of quasi-harmonic oscillator via approximate point mapping

At present, there is no particular need to justify the importance of oscillatory processes in modern physics and natural science. The apparatus of the theory of differential equations is a recognized tool for studying oscillatory processes in various branches of physics and engineering. Naturally, oscillatory systems with low nonlinearity are the most accessible for research and in so far, the study of systems close to the harmonic oscillator (quasi-harmonic oscillator) presents particular interest. The article explores the possibility of reducing the problem of studying the synchronization of a quasi-harmonic oscillator to the study of the Poincare functions of a point map, which is constructed using the method of successive approximation. The article concludes that the results of the study of the system as a whole depend on the type of nonlinearity.