On the role of internal interactions within a nonlinear coupler in the Leggett–Garg inequality violation

In this work, we investigate the influence of the internal interactions within the nonlinear oscillatory system on its ability to lead to the violation of the Leggett-Garg inequality when performing a set of projective measurements. We emphasize the crucial role in selecting an appropriate time interval between the consecutive projections and show that, for some types of internal interactions that effectively confine the system's dynamics to only a few states, there are entire ranges of parameters characterizing the system for which the inequality cannot be violated.