Phase Space Reconstruction from Time Series Data: Where History Meets Theory

Abstract

In ‘dissipative’ dynamical systems, variables evolve asymptotically toward low

dimensional ‘attractors’ that define their dynamical properties. Unfortunately, real‐world dynamical systems are generally too complex for us to directly observe these attractors. Fortunately, there is a method—‘phase space reconstruction’—that can be used to indirectly detect attractors in real‐world dynamical systems using time series data on a single variable (Broomhead and King, 1985; Schaffer and Kott, 1985; Kott et al, 1988; Williams,1997). Armed with this knowledge, we can formulate more accurate and informative models of real‐world dynamical systems.