Detection and Reconstruction of Bursting Oscillations in Complex Systems Using the HAVOK Analysis Framework

Multi-scale dynamical systems may exhibit bursting oscillations, which are typically identified by analyzing time series and phase portraits. However, in cases where bursting oscillations are not apparent, relying solely on these methods may have limitations in accurately detecting their occurrence. This paper introduces the HAVOK analysis framework to the field of bursting oscillations. By using single-variable time series data, models that may produce bursting oscillations are restructured into forced linear models. This approach allows for the rapid prediction of bursting oscillations by observing the forced terms. The results show that the intermittent periodic bursts in the visualizations of the forced eigen time series within the HAVOK framework are strongly correlated with the excitation states in bursting oscillations, enabling the prediction of their occurrence. Especially in cases where it is challenging to determine the presence of bursting oscillations through time series plots alone, this method can still sensitively detect them. Additionally, the embedded and reconstructed flow fields plotted using this approach can help understand the dynamics of bursting oscillations in certain scenarios.