Figure 5.

Increasing sampling frequency and number of columns yields more structured HAVOK models for the Lorenz system. Given the Hankel matrix $\mathit{H}$, the linear dynamical model is plotted for values of sampling period $\mathrm{\Delta }t$ equal to 0.01, 0.005, 0.001, 0.0005 for a fixed number of rows and fixed time span of measurement (a–d). Similarly, the model is plotted for values of the number of columns $n$ equal to 1001, 2001, 5001 and $10\hspace{0.17em}001$ for fixed sampling frequency and number of delays $m$ (e–h). As we increase the sampling frequency and the number of columns of the data, $\mathit{A}$ becomes more antisymmetric with non-zero elements only on the super- and sub-diagonals. These trends illustrate the results in §4. (Online version in colour.)