Exploring recursive properties and dynamical complexity in scalar time-series using threshold-free recursive analysis approach

In this project, a threshold-free recursive analysis approach was investigated to reveal the recursive properties of dynamic systems. Specifically, the occurrence of recurrent patterns in phase trajectory was identified by a threshold-free recursive matrix whose elements would possess continuous values within the interval of [0, 1] and are inversely proportional to the distance between phase points. Subsequently, mapping and feature extraction were carried out to visualize and quantify the threshold-free recursive matrix. Theoretical time-series, along with observed time-series in the fields of engineering, finance, and hydrology, have been utilized to validate the efficacy of this approach. The results demonstrate the applicability of this method in analyzing the dynamic characteristics of scalar time-series. Furthermore, the rebuilt grayscale recurrence plot morphology and extracted measures through grayscale recurrence quantification analysis measures can effectively unveil the dynamical complexity of nonlinear systems by offering more precise analysis outcomes for investigating the evolution of recursive characteristics.