Compressing Phase Space Detects State Changes in Nonlinear Dynamical Systems

Figure 1

Estimated embedding dimensions for low-dimensional chaotic system. (a) First derivative of as a function of at different time delays for a Lorenz dynamical system. Across all values, the derivative reaches zero for . (b) Estimated for a set of chaotic systems. For comparison purposes, values are plotted as a function of correlation dimension . For each dynamical system, we show mean and standard error of the mean evaluated across realizations. Dashed line corresponds to ; dotted line is .

(a)

(b)