how to plot Bifurcation Diagram of chaotic map

How to plot bifurcation diagram for 3 variables x,y and z of the following chaotic map:

numsteps = 1000; % number of steps to iterate
a=0.9; b=-0.6013; c=2; d=0.5; % fix conditions
x(1) = -0.72; y(1) = -0.64; z(1)=0.5; %initial values
for i = 1:numsteps; 
x(i+1) = (x(i)).^2 - (y(i)).^2 + a*x(i)+b*y(i);
y(i+1) = 2*x(i)*y(i) + c*x(i) + d*y(i); 
z(i+1) = sin(3.5*z(i));
end

Answer 1

[Jim Riggs]

You can plot all of the data in 3 dimensions using

figure;
plot3(x,y,z,'ob')

This will create a 3D plot using a marker at each data point. You can then rotate the group of points in the figure window to see the patern from different perspectives using the "Rotate 3D" button at the top of the figure window.

This pattern is only visible in the X-Y plane, so you need to rotate the 3D plot so that you are viewing from the top.

An alternative is to just make a 2D plot using the x and y data:

figure;
plot(x,y,'ob')

(Also, since you are using a fixed number of steps for the loop, you should preallocate your vectors, e.g.

clear x y z;
numsteps=1000;
x = zeros(numsteps+1,1);
y = zeros(numsteps+1,1);
z = zeros(numsteps+1,1);
...

[tanveer haq]

what will be its lyapunov exponent digram?