In-band supratransmission in nonlinear flat band lattices

Abstract: 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.