Bifurcation values for logistic map

[sumonmumu]

Homework Statement

Find numerically the r values for the first 2 bifurcations.

Homework Equations

xi+1 = f(xi), f(x) = rx(1 − x)

The Attempt at a Solution

To find the values of r, first I set rx(1−x)=0 to find x and then used the x values to find r=0 and r=1. But, I am still confused. Do you think what I did here is correct? If not, can you help me find the mistakes here?

 

[mfb]

first I set rx(1−x)=0 to find x

Why =0? What is special about 0?

 

[sumonmumu]

To find the bifurcation value, you have to set dx/dt = 0. That's the speciality.

 

[mfb]

dx/dt = 0 is different from your equation.

 

[sumonmumu]

f(x) = dx/dt here.

 

[mfb]

Okay, then I don't understand your notation, but f(x)=0 is nothing special just because there is a zero.

and then used the x values to find r=0 and r=1

And I don't understand how you got that.