Emergence and mitigation of extreme events in a parametrically driven system with velocity-dependent potential

In this paper, we discuss the emergence of extreme events in a parametrically driven non-polynomial mechanical system with a velocity-dependent potential. We confirm the occurrence of extreme events from the probability distribution function of the peaks, which exhibits a long-tail. We also present the mechanism for the occurrence of extreme events. We found that the probability of occurrence of extreme events alternatively increases and decreases with a brief region where the probability is zero. At the point of highest probability of extreme events, when the system is driven externally, we find that the probability decreases to zero. Our investigation confirms that the external drive can be used as an useful tool to mitigate extreme events in this nonlinear dynamical system. Through two-parameter diagrams, we also demonstrate the regions where extreme events get suppressed. In addition to the above, we show that extreme events persist when the system is influenced by noise and even get transformed to super-extreme events when the state variable is influenced by noise.