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Recursion


Dear Sirs,

I would like to obtain trajectories with respect to x, from the following
relationship:
               
               

                    x(t+1)=a x(t)(1-x(t))

 

Here, a means a constant with a constraint, 1 < a < 4, t   a positive integer 
and x a variable.
I know this difference equation cannot be solved by mathematics directly, 
because it is not linear.
So, I would like to follow a numerical series in terms of x, and I need to 
know how to program Mathematica for this.

I look forward to your response.

     

     Sincerely,
     
     Fujio Takata.


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