Logistic Map Bifurication Diagram

Trying to plot the logistic map bifurication diagram, but keep getting errors... can someone take a look at this and tell me where I am going wrong.

c=0; 
y=0.0;  

hold on 
while c < 1
        for i=1:100; 
            y = -c*y.^2 +c*y.; %converge the iteration
        end 
        for i=1:20 

              y = -c*y.^2 +c*y.;
              plot(c,y,'.', 'MarkerSize',1); % plot the converged points
          end 
          c=c+0.002;
  end

Answer 1

[David Young]

There are various problems:

There's a syntax error due to the dot at the end of

y = -c*y.^2 +c*y.;

Since y is a scalar, you can just omit the dot, and use

y = -c*y.^2 +c*y;

c in the range 0 to 1 produces uninteresting behaviour - to see bifurcation you could scan c through the range 2.8 to 4.

y needs to be initialised inside the outer loop (after the while) otherwise it just starts from whatever the previous value was. However, initialising to 0 (or to 1) will produce uninteresting behaviour. Try initialising y to 0.5.

With these changes, you can get a bifurcation plot.