We analyze the temporal dynamics associated with the jet-flap interactions by carrying-out a dynamical-systems analysis. The experimental cases are characterized by three different setups of the jet-flap system, running in the range M a = 0.6 − 1.0. The analysis is based on data presented by Jordan et al., 1 where the self-sustained oscillations were analyzed by means of linear models. Nonlinear competition among the modes was observed: here we analyze this interplay by investigating the system using statistical tools, phase portraits, Poincaré sections, and return maps. We estimate the minimal number of degrees of freedom necessary for the description of a nonlinear model. The correlation dimension is assessed for four representative cases. Finally, we analyze the toroidal geometry in the phase-space and identify the main ingredients necessary for nonlinear reduced-order models of this system.