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Bifurcation values for logistic map

  1. Mar 20, 2014 #1
    1. The problem statement, all variables and given/known data

    Find numerically the r values for the first 2 bifurcations.

    2. Relevant equations

    xi+1 = f(xi), f(x) = rx(1 − x)
    3. 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?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Mar 20, 2014 #2

    mfb

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    Staff: Mentor

    Why =0? What is special about 0?
     
  4. Mar 20, 2014 #3
    To find the bifurcation value, you have to set dx/dt = 0. That's the speciality.
     
  5. Mar 20, 2014 #4

    mfb

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    Staff: Mentor

    dx/dt = 0 is different from your equation.
     
  6. Mar 20, 2014 #5
    f(x) = dx/dt here.
     
  7. Mar 20, 2014 #6

    mfb

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    2016 Award

    Staff: Mentor

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

    And I don't understand how you got that.
     
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