Calculate line length distributions of a recurrence plot
In the following example we use the Roessler system and the commandline RP software.
Contents
For the Roessler ODE we need to prepare a file roessler.m with the following content:
function dy=roessler(t,y, dummy, abc) dy=zeros(3,1);
if nargin < 4 a=.2; b=.2; c=5.7; else a = abc(1); b = abc(2); c = abc(3); end
dy(1)=-y(2)-y(3); dy(2)=y(1)+a*y(2); dy(3)=b+y(3)*(y(1)-c);
The commandline RP file should be copied into the current working folder. Here we use a Linux version of it with the name rp_x86_64i. You should modify accordingly to your system and version.
Line length distribution for Roessler Fig. 26A
clear options=odeset('initialstep',.01,'MaxStep',.1);
sampling time difference is 0.2
time=0:.2:2050;
integrate Roessler system roessler_abc = [0.2 0.2 5.7];
[t, x]=ode45('roessler',time,[0.1 0.4 0.3],options);
save data as 3-column vector, ASCII file
x1 = x(251:end,:); save roessler x1 -ascii -tabs
calculate the recurrence plot and cumulative line length distribution using commandline RP tool
clear, e = 0.862
unix(['./rp_x86_64i -n MAX -w 2 -i roessler -c -p roessler_hist -e ',num2str(e)]);
e =
0.8620
Used file: [1mroessler[0m (30003 data points in 3 columns read).
Used parameters: embedding dimension m = 1
embedding delay t = 1
recurrence threshold e = 0.862
Theiler window w = 2
minimal diagonal line l_min = 2
minimal vertical line v_min = 2
maximum norm used
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Computation time: 0 min 2 sec
Recurrence quantification analysis:
RR: 0.009573
DET: 0.9717 LAM: 0.522
DET/RR: 101.5 LAM/DET: 0.5372 W_prob: 87
L_max: 404 V_max: 4 W_max: 5241
L_mean: 14.02 TT: 2.255 W_mean: 140.9
L_entr: 3.048 V_entr: 0.6153 W_entr: 3.26
DIV: 0.002475 T1: 101.9 F_min: 0.0001908
T2: 144.2
load histogram into Matlab
h=load(['roessler_hist']); p = h(:,2);
plot the histogram
clf semilogy(1:200,p(1:200,1:4:end),'k'), xlim([1 200]) xlabel('Length l (units)'), ylabel('Total number') set(gca,'xtick',[0:50:200],'xtickl',[0:50:200]), ylim([1e1 1e8])
Line length distribution for Roessler Fig. 27
integrate Roessler system
clear,options=odeset('initialstep',.01,'MaxStep',.1);
sampling time difference is 0.2
time=0:.2:2050;
Roessler with C = 9
roessler_abc = [0.1 0.1 9];
[t, x]=ode45('roessler',time,[0.1 0.4 0.3],options,roessler_abc);
save data as 3-column vector, ASCII file
x1 = x(251:end,:); save roessler9 x1 -ascii -tabs
Roessler with C = 30
roessler_abc = [0.1 0.1 30];
[t, x]=ode45('roessler',time,[0.1 0.4 0.3],options,roessler_abc);
save data as 3-column vector, ASCII file
x1 = x(251:end,:); save roessler30 x1 -ascii -tabs
calculate the recurrence plot and cumulative line length distribution using commandline RP tool, first for C = 30
clear, e = 2; unix(['./rp_x86_64i -s -n MAX -w 2 -i roessler30 -c -p roessler_hist -e ',num2str(e)]); h=load(['roessler_hist']); p(:,1) = h(:,2);
next for C = 9
unix(['./rp_x86_64i -s -n MAX -w 2 -i roessler9 -c -p roessler_hist -e ',num2str(e)]); h=load(['roessler_hist']); p(:,2) = h(:,2);
finally plot the histogram
clf semilogy(.2*(6:200),p(6:200,1),'k--'), hold on semilogy(.2*(6:200),p(6:200,2),'k-') xlabel('Length l (s)'), ylabel('Total number') yl = ylim;line([12 12],yl,'linestyle',':','color',[0 0 0]) line([24.8 24.8],yl,'linestyle',':','color',[0 0 0])
