Graphics Programs Reference
In-Depth Information
Integrating the differential equation yields a simple MATLAB code for
computing the
xyz
triplets of the Lorenz attractor. As system parameters
controlling the chaotic behaviour we use
s=10
,
r=28
and
b=8/3
, the time
delay is
dt=0.01
. The initial values are
x1=6
,
x2=9
and
x3=25
,
that can
certainly be changed at other values.
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
Typical traces of a variable, such as the fi rst variable can be viewed by
plotting
x(:,1)
over time in seconds (Fig. 5.12).
Lorenz System
20
15
10
5
0
−5
−10
−15
−20
0
5
10
15
20
25
30
35
40
45
50
Time
Fig. 5.12
The Lorenz system. As system parameters we use
s=10
,
r=28
and
b=8/3
, the
time delay is
dt=0.01
.
