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Re: Recursion

• To: mathgroup at smc.vnet.net
• Subject: [mg62309] Re: Recursion
• From: Bill Rowe <readnewsciv at earthlink.net>
• Date: Sat, 19 Nov 2005 23:18:35 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

On 11/19/05 at 5:53 AM, JikaiRF at aol.com wrote:

>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.

This can be accomplished with NestList, i.e.,

NestList[a #(1-#)&, t, n]

will list of n+1 items with the first being t and each subsequent term being ax(1-x) where x is the preceding term.

Another possiblility is

FixedPointList[a #(1-#)&, t]

This will return a list that ends with the last two elements being the same *assuming* a is chosen so there is convergence. 
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