Two-oscillator model of trapped-modes interaction in a nonlinear bilayer fish-scale metamaterial

We discuss a similarity between resonant oscillations in two nonlinear systems; namely, a chain of coupled Duffing oscillators and a bilayer fish-scale metamaterial. In such systems two different resonant states arise which differ in their spectral lines. The spectral line of the first resonant state has a Lorentzian form, whereas the second one has a Fano form. This difference leads to a specific nonlinear response of the systems which manifests itself in the appearance of closed loops in spectral lines and bending and overlapping of resonant curves. Conditions for achieving bistability and multistability are determined.