In-band supratransmission in nonlinear flat band lattices

Studying wave propagation in nonlinear discrete systems is essential for understanding energy transfer in lattices. While linear systems prohibit wave propagation within the natural band gap, nonlinear systems exhibit {supratransmission}, enabling energy transfer above a critical driving amplitude. This work investigates novel \emph{in-band supratransmissions} for waves with frequencies in a \emph{flat} or \emph{nearly flat} linear band. Flat bands, characterized by zero group velocity and localized modes due to destructive interference, provide an ideal framework for studying wave confinement and energy dynamics. In-band supratransmission originates from a bifurcation of evanescent waves at the flat band frequency. Using nonlinear \emph{diamond} and \emph{stub} lattices as model systems, we explore how lattice topology, nonlinearity, and driving amplitude affect supratransmission. Through bifurcation analysis, stability evaluations, and time-dependent simulations, we examine the transition from energy localization to supratransmission.