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S = zeros(N, N);
for i = 1 : N,
S(:,i) = abs(repmat(series1L(i), N, 1 ) - series1L(:));
end
We can now plot the distance matrix
imagesc(t,t,S)
colormap jet
colorbar
xlabel('Time'), ylabel('Time')
axis xy
for the data set, where a colorbar provides a quantitative measure of the
distances between states (Fig. 5.23). We now apply a threshold ʵ to the
distance matrix to generate the black/white recurrence plot (Fig. 5.24).
imagesc(t,t,S<1)
colormap([1 1 1;0 0 0])
xlabel('Time'), ylabel('Time')
axis xy
Both plots reveal periodically recurring patterns. h e distances between
these periodically recurring patterns represent the cycles contained in the
time series. h e most signii cant periodic patterns have periods of 200
and 100 kyrs. h e 200 kyr period is the most signii cant because of the
superposition of the 100 and 40 kyr cycles, which are common divisors of
200 kyrs. Moreover, there are smaller substructures within the recurrence
plot that have periods of 40 and 20 kyrs.
As a second example we now apply the method of recurrence plots to the
Lorenz system. We again generate xyz triplets from the coupled dif erential
equations.
clear
dt = .01;
s = 10;
r = 28;
b = 8/3;
x1 = 8; x2 = 9; x3 = 25;
for i = 1 : 5000
x1 = x1 + (-s*x1*dt) + (s*x2*dt);
x2 = x2 + (r*x1*dt) - (x2*dt) - (x3*x1*dt);
x3 = x3 + (-b*x3*dt) + (x1*x2*dt);
x(i,:) = [x1 x2 x3];
end
We then choose the resampled i rst component of this system and reconstruct
a phase space trajectory by using an embedding of m =3 and ˄=2.
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