  We study the dynamics of a parametrically and externally driven
Rayleigh-Lienard hybrid model and report the emergence of extreme bursting
events due to a novel pulse-shaped explosion mechanism. The system exhibits
complex periodic and chaotic bursting patterns amid small oscillations as a
function of excitation frequencies. In particular, the advent of rare and
recurrent chaotic bursts that emerged for certain parameter regions is
characterized as extreme events. We have identified that the appearance of a
sharp pulse-like transition that occurred in the equilibrium points of the
system is the underlying mechanism for the development of bursting events.
Further, the controlling aspect of extreme events is attempted by incorporating
a linear damping term, and we show that for sufficiently strong damping
strength, the extreme events are eliminated from the system, and only periodic
bursting is feasible.
