  Extensive dynamical simulations are used to explore the possible existence of
sudden sufficiently large energy or rogue fluctuations (RF) at late times and
across short time windows in the {\it strongly nonlinear regime} of the
$\beta$-Fermi-Pasta-Ulam-Tsingou (FPUT) type systems. Our studies build on a
study of RF in the non-dissipative granular chain system and suggest that {\it
rare RF may be generic to non-integrable, strongly nonlinear systems at late
enough times}. We comment on the role of initial conditions and the intriguing
influence of harmonic forces on these strongly nonlinear systems. The RF under
focus here are distinct from the well known Peregrine solitons used to describe
rogue waves via the weakly nonlinear Schr\"odinger equation.
