受迫Van der Pol广义振子模型下系统振荡的非线性动力学
Nonlinear dynamics of system oscillations modeled by a forced Van der Pol generalized oscillator
摘要：
本文研究了受迫Van der Pol广义振子模型的振动。这些振荡的形式$ \ddot{x}+x-\varepsilon\left(1-ax^2-b\dot{x}^2\right)\dot{x}=E\sin{Ωt}.$的非线性微分方程描述的强迫谐波，主共振超谐波和亚谐波振荡状态的振幅使用谐波平衡技术和多时间尺度方法获得。我们还得到了系统振荡的滞后和跳跃现象。通过四阶龙格-库塔格式数值模拟了每种振荡状态下模型所显示的分岔序列。
英文摘要：
This paper considers the oscillations modeled by a forced Van der Pol generalized oscillator. These oscillations are described by a nonlinear differential equation of the form $ \ddot{x}+x-\varepsilon\left(1-ax^2-b\dot{x}^2\right)\dot{x}=E\sin{Ωt}.$ The amplitudes of the forced harmonic, primary resonance superharmonic and subharmonic oscillatory states are obtained using the harmonic balance technique and the multiple time scales methods. We obtain also the hysteresis and jump phenomena in the system oscillations. Bifurcation sequences displayed by the model for each type of oscillatory states are performed numerically through the fourth-order Runge- Kutta scheme.
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