Geoscience Reference
In-Depth Information
b
a
Fig. 5.19 a
Original, and
b
reconstructed phase space portrait for a periodic system. h e
reconstructed phase space is almost the same as the original phase space.
system are described by three coupled nonlinear dif erential equations:
Integrating the dif erential equation yields a simple MATLAB code for
computing the
xyz
triplets of the Lorenz system. As system parameters
controlling the chaotic behavior we use
s=10
,
r=28
and
b=8/3
; the time delay
is
dt=0.01
. h e initial values for the position vectors are
x1=8
,
x2=9
and
x3=25
.
h ese values, however, can be changed to any other values, which of course
will then change the behavior of the system.
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
