Why matlab giving me same values too many times

Ok my input function was

r=2;
x(1)=0.3;
N=100
for i=1:N
x(i+1)=r*x(i)*(1-x(i))
end

And, matlab calculated my answer but gave me the same x values for about 6 times. It's very annoying since I don't need the same x values over and over again. Please tell me how can I avoid that? Thanks.

[Azzi Abdelmalek]

What are you expecting?

[Sam]

I am expecting to avoid the same values over and over again.

Answer 1

[Mischa Kim]

Sumon, I think you are referring to fact that the series approaches x = 0.5 for increasing i. This is absolutely to be expected. For small x the linear term dominates which leads to an increase in x. However, as x is increasing the quadratic term starts to become more prevalent up to a point, where they will balance each other out. This point is "reached" when

 x(i) = r*x(i)*(1-x(i))

or, put aside the indices,

 x = r*x*(1 - x)
 1 = r*  (1 - x)

or, solving for x

 x = (r - 1)/r = 0.5

At that point, the values for x(i) remain constant, x(i+1) = x(i).

[Sam]

Oh I get it now. Thanks for clearing things up for me.

[Walter Roberson]

In theory you only get x = 1/2 if your start with x = 1/2 . But in practice when you start with x in the range 0 to 1 exclusive then within a few steps the loss of precision will get you to floating point 0.5 after which it will stay there.

Answer 2

[Walter Roberson]

MATLAB uses finite precision floating point binary numbers. After a few steps of the calculation, all of the answers are the same to within the limited precision. If you require increased precision then you will need to use something like the symbolic toolbox.

x(t) = -1/2*((2/5)^(2^(t-1))-1)