So here are the solutions
to quiz 2 from Unit 5.2
The first questioned asked about
r equals 1.8
What value is the fixed point?
So, I will zoom in here.
It looks like this region has 1.8 in it.
Zoom in a little bit.
And now I'm going to move the cursor
Until the r value is about 1.8
Then I will see what the x value is.
So, here where my cursor is
r is a little more than 1.8
and I see that the x value there is 0.436
So about 0.44
So the best answer to this question was 0.44
There is a fixed point at around .44 when r is 1.8
The next question asked about bifurcation
from period two to period four.
So I'm going to go back
and I'm going to zoom in here.
So bifurcation from period 2 to period 4
that occurs around here.
So when there are two lines
if you go up from here
and the line crosses
this imaginery line intersects two lines
in the bifurcation diagram
that means it would be
a final state diagram
with two dots
Here we go up we cross through four
so it is period four.
The transition occurs here
Here.
And that looks to be about 3.44, 3.45.
So that gives us an approximate r value
where this bifurcation occurs.
The last question, question 3.
Asked what goes on around 3.906.
There is a periodic window
of what period
So let me go back one.
And this will take a little bit
of trial and error exploration.
So let me zoom in.
3.9 where is that.
That looks to be around here.
I want 3.906. Let's try zooming in.
Here. Update again.
3.906.
3.906
Here is around 3.906
You can tell because
I'm reading this mouse position here.
Let's see 1,2,3,4,5.
So I see period five behavior here.
So this is a window of period five.
So, near r equals 3.906.
There is a periodic window
of period five.