We study the dynamics of a Duffing oscillator excited by correlated random perturbations for both fixed and periodically modulated stiffness. In the case of fixed stiffness we see that Poincaré map gets distorted due to the random excitation and, the distortion increases with the increase of correlation of the field. In a strongly correlated field, however, the map becomes purely random. We analyse the maximum value of the Lyapunov exponent and see that the random response competes with the chaotic motion to increase the stability of the system. In the case of periodically modulated stiffness, the periodic parametric excitation causes the Duffing system to execute dynamics of two fixed-point attractors. These attractors remain non-chaotic even in the presence of random field but can get merged due to induced fluctuation in the trajectory. It is seen that the random field can change the status of the system from transit to stable state.

中文翻译：

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随机激励对达芬系统动态响应的影响

我们研究了由固定和周期性调制刚度的相关随机扰动激发的 Duffing 振荡器的动力学。在固定刚度的情况下，我们看到庞加莱图由于随机激励而扭曲，并且随着场相关性的增加，扭曲增加。然而，在强相关领域，地图变得纯粹随机。我们分析了李雅普诺夫指数的最大值，发现随机响应与混沌运动竞争以增加系统的稳定性。在周期性调制刚度的情况下，周期性参数激励导致 Duffing 系统执行两个定点吸引子的动力学。即使在存在随机场的情况下，这些吸引子也保持非混沌状态，但由于轨迹中的诱导波动而可能合并。