标题： 常数偏置和弱第二周期扰动：减轻极端事件的工具 显示英文标题

标题： 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）恒定偏置和（ii）弱二次周期强迫，作为缓解极端事件的工具。 我们展示了这两种工具在抑制两个著名的非线性动力系统中的极端事件的有效性，即（i）Liénard系统和（ii）具有速度相关势能的非多项式机械系统。 就恒定偏置而言，在Liénard系统中，抑制是由于大振幅振荡的减少，在非多项式机械系统中，抑制是由于混沌被破坏为周期轨道。 就二次周期强迫而言，在两个例子中，极端事件由于大振幅振荡的增加而得到抑制。 我们还证明，通过在二次周期强迫中引入相位，可以在非多项式系统中进一步降低极端事件发生的概率。 为了支持极端事件的完全抑制，我们为所有情况提供了二维概率图。 除了上述内容外，我们还检查了上述工具在非多项式机械系统的参数驱动版本中的可行性。 最后，我们研究了这两种方法如何影响Liénard系统中的多稳定性特性。 显示英文摘要

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) Li\'enard system and (ii) a non-polynomial mechanical system with velocity dependent potential. As far as the constant bias is concerned, in the Li\'enard 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 Li\'enard system.