恒定偏置和弱第二周期强迫：缓解极端事件的工具
Constant Bias and Weak Second Periodic Forcing : Tools to Mitigate Extreme Events
摘要：
我们提出了两种潜在可行的非反馈方法，即（i）恒定偏差和（ii）弱第二周期强迫作为缓解极端事件的工具。我们证明了这两个工具在抑制两个著名的非线性动力系统，即（i）Liénard系统和（ii）与速度相关的潜在的非多项式力学系统的极端事件的有效性。在Liénard系统中，由于大振幅振荡的减少而发生抑制;在非多项式力学系统中，由于混沌被破坏成周期轨道而发生抑制。就第二周期强迫而言，在这两个例子中，极端事件得到抑制，由于大振幅振荡的增加。我们还表明，通过引入一个阶段，在第二个周期强迫可以降低极端事件发生的概率，甚至进一步在非多项式系统。为了给极端事件的完全抑制提供支持，我们给出了所有情况下的双参数概率图。除了上述，我们研究的可行性，上述工具中的参数驱动版本的非多项式机械系统。最后，我们研究了这两种方法如何影响Liénard系统的多稳定性。
英文摘要：
We propose two potentially viable non-feedback methods, namely (i) constant bias and (ii) weak second periodic forcing as tools to mitigate extreme events. We demonstrate the effectiveness of these two tools in suppressing extreme events in two well-known nonlinear dynamical systems, namely (i) Liénard system and (ii) a non-polynomial mechanical system with velocity dependent potential. As far as the constant bias is concerned, in the Liénard system, the suppression occurs due to the decrease in large amplitude oscillations and in the non-polynomial mechanical system the suppression occurs due to the destruction of chaos into a periodic orbit. As far as the second periodic forcing is concerned, in both the examples, extreme events get suppressed due to the increase in large amplitude oscillations. We also demonstrate that by introducing a phase in the second periodic forcing one can decrease the probability of occurrence of extreme events even further in the non-polynomial system. To provide a support to the complete suppression of extreme events, we present the two parameter probability plot for all the cases. In addition to the above, we examine the feasibility of the aforementioned tools in a parametrically driven version of the non-polynomial mechanical system. Finally, we investigate how these two methods influence the multistability nature in the Liénard system.
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