In this work, we implement multiplicative noise to the Duffing oscillator with variable coefficients. The stochastic differential equations are solved using the fourth-order Runge–Kutta method with the Box-Müller algorithm and the corresponding integral of motion is obtained. Some numerical experiments are performed and the results show that the integral of motion is highly unaffected by the multiplicative noise.

中文翻译：

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乘性噪声对变系数达芬振子及其运动积分的影响

在这项工作中，我们对具有可变系数的 Duffing 振荡器实现了乘性噪声。使用 Box-Müller 算法的四阶 Runge-Kutta 方法求解随机微分方程，并获得相应的运动积分。进行了一些数值实验，结果表明运动的积分不受乘性噪声的影响。