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5.6 Nonlinear Time-Series Analysis (by N. Marwan) 113

for the data set. Adding a colorbar

colorbar
provides a quantitative measure for the distances between states (Fig. 5.14).
We apply a threshold ε to the distance matrix to generate the black/white
recurrence plot (Fig. 5.15).

imagesc(t,t,S<1)
colormap([1 1 1;0 0 0])
xlabel('Time'), ylabel('Time')

Both plots reveal periodically occurring patterns. The distances between
these periodic patterns represent the cycles contained in the time series. The
most significant periodic structures have periods of 200 and 100 kyr. The 200

kyr period is most significant because of the superposition of the 100 and 40
kyr cycles, which are common divisors of 200 kyr. Moreover, there are small

0

100

200

300

400

500

600

700 6.0

800 4.0

900 2.0

0.0
0 100 200 300 400 500 600 700 800 900
Fig. 5.14 Visualization of the distance matrix from the synthetic data providing a quantitative
measure for the distances between states at certain times; blue colors indicate small distances,
red colors represent large distances.