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

Are rare rogue fluctuations generic to strongly nonlinear and non-integrable systems?