Artificial and Real-World Chaotic Oscillators

Four archetypal chaotic maps are used to generate the noise-free synthetic datasets for the forecasting task: the logistic and the Hénon maps, which are the prototypes of chaos in non-reversible and reversible systems, respectively, and two generalized Hénon maps, which represent cases of low- and high-dimensional hyperchaos. We also present a modified version of the traditional logistic map, introducing a slow periodic dynamic of the growth rate parameter, that includes ranges for which the map is chaotic. The resulting system exhibits concurrent slow and fast dynamics and its forecasting represents a challenging task. Lastly, we consider two real-world time series of solar irradiance and ozone concentration, measured at two stations in Northern Italy. These dynamics are shown to be chaotic movements by means of the tools of nonlinear time-series analysis.