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We propose two potentially viable non-feedback methods, namely (i) constantbias and (ii) weak second periodic forcing as tools to mitigate extreme events.We demonstrate the effectiveness of these two tools in suppressing extremeevents in two well-known nonlinear dynamical systems, namely (i) Li\'enardsystem and (ii) a non-polynomial mechanical system with velocity dependentpotential. As far as the constant bias is concerned, in the Li\'enard system,the suppression occurs due to the decrease in large amplitude oscillations andin the non-polynomial mechanical system the suppression occurs due to thedestruction of chaos into a periodic orbit. As far as the second periodicforcing is concerned, in both the examples, extreme events get suppressed dueto the increase in large amplitude oscillations. We also demonstrate that byintroducing a phase in the second periodic forcing one can decrease theprobability of occurrence of extreme events even further in the non-polynomialsystem. To provide a support to the complete suppression of extreme events, wepresent the two parameter probability plot for all the cases. In addition tothe above, we examine the feasibility of the aforementioned tools in aparametrically driven version of the non-polynomial mechanical system. Finally,we investigate how these two methods influence the multistability nature in theLi\'enard system.

Constant Bias and Weak Second Periodic Forcing : Tools to Mitigate Extreme Events