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We propose a general strategy for reduced order modeling of systems thatdisplay highly nonlinear oscillations. By considering a continuous family offorced periodic orbits defined in relation to a stable fixed point andsubsequently leveraging phase-amplitude-based reduction strategies, we arriveat a low order model capable of accurately capturing nonlinear oscillationsresulting from arbitrary external inputs. In the limit that oscillations aresmall, the system dynamics relax to those obtained from local linearization,i.e.,~that can be fully described using linear eigenmodes. For larger amplitudeoscillations, the behavior can be understood in terms of the dynamics of asmall number of nonlinear modes. We illustrate the proposed strategy in avariety of examples yielding results that are substantially better than thoseobtained using standard linearization-based techniques.

Reduced Order Characterization of Nonlinear Oscillations Using an Adaptive Phase-Amplitude Coordinate Framework