The paper investigates a modified van der Pol equation with hysteresis nonlinearity which is formalized within the Preisach approach. The system considered in the work is a mathematical model of an electrical system similar to the classical van der Pol system where characteristics of the nonlinear part are of hysteresis nature. The main method for studying this system is the classical small parameter approach. Within this method, an analytical solution to the equation describing the system under consideration was obtained. Numerical results are presented and a comparative analysis of the dynamics of the system under consideration with the dynamics of the classical van der Pol oscillator is carried out. Dynamic modes of the modified oscillator are investigated depending on the parameters of the system. Spectral characteristics are also compared to the corresponding characteristics of the classical van der Pol oscillator.

本文研究了在 Preisach 方法中形式化的具有滞后非线性的修正 van der Pol 方程。工作中考虑的系统是类似于经典 van der Pol 系统的电气系统的数学模型，其中非线性部分的特性具有滞后性质。研究该系统的主要方法是经典的小参数方法。在该方法中，获得了描述所考虑系统的方程的解析解。给出了数值结果，并对所考虑的系统动力学与经典范德波尔振荡器的动力学进行了比较分析。根据系统参数研究改进振荡器的动态模式。