In this paper, nonlinear dynamics study of a RLC series circuit modeled by a generalized Van der Pol oscillator is investigated. After establishing a new general class of nonlinear ordinary differential equation, a forced Van der Pol oscillator subjected to an inertial nonlinearity is derived. According to the external excitation strength, harmonic, subharmonic and superharmonic oscillatory states are obtained using the multiple time scales method. Bifurcation diagrams displayed by the model for each system parameter are performed numerically through the fourth-order Runge–Kutta algorithm.

中文翻译：

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由广义范德波尔振荡器建模的 RLC 串联电路的非线性动力学

在本文中，研究了由广义范德波尔振荡器建模的 RLC 串联电路的非线性动力学研究。在建立了一类新的非线性常微分方程后，推导出受惯性非线性作用的强迫Van der Pol振子。根据外部激励强度，采用多时间尺度方法获得谐波、次谐波和超谐波振荡状态。模型为每个系统参数显示的分岔图通过四阶 Runge-Kutta 算法进行数值计算。