Fig. 2

Visualization of the minimum radius selection using single realizations of Fitzhugh-Nagumo data with 512 timepoints at three different noise levels. Dashed lines indicate the minimum radius \({\underline{m}}_t\) Left: we see that inequality (20) holds empirically for small radii \(m_t\). Right: coefficient error \(E_2\) as a function of \(m_t\) is plotted, showing that for each noise level the identified radius \(m_t\) using \({\hat{\textbf{e}}}_\text {rms}\) lies to right of the dip in \(E_2\), as random errors begin to dominate integration errors. In particular, for low levels of noise, \({\underline{m}}_t\) increases to ensure high accuracy integration