Data-driven model identification using forcing-induced limit cycles

This paper presents a data-driven model identification strategy that characterizes the behavior of a general dynamical system relative to a set of limit cycles that emerge in response to periodic forcing. Using time series data to infer the phase-amplitude dynamics associated with the underlying forced limit cycles, a low-order model can be obtained that accurately captures the dynamical behavior in response to arbitrary external inputs. The proposed strategy can be readily implemented in situations where full state measurements are unavailable and does not require any prior knowledge of the underlying model equations. This technique is applied to a model of coupled planar oscillators and to a model that considers the spike rate in a population of coupled conductance-based neurons where it outperforms two other commonly used data-driven model identification techniques.