Figure 4.

Results of simulation of second order differential equations with signal to noise ratio of 2:1, $N=300$, $\eta =-.5$, and $\zeta =-.1$ resulting in 30 observations per cycle as fit with second order and constrained fourth order models for 12 different embedding dimensions. (a) Second order model estimated $\eta$ parameter for each selected embedding dimension. Simulated $\eta =-.5$ is shown as horizontal line. Mean and standard deviation of the estimated parameters are plotted for all models that converged. (c) Second order approximation results for $\zeta =-.1$. (e) Percent of models that converged (green), did not converge (red), and stopped due to exceeding the maximum iterations. (b,d,f) The $\eta$, $\zeta$, and convergence percentages for the constrained fourth order model.