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Re: Recursion

• To: mathgroup at smc.vnet.net
• Subject: [mg62310] Re: Recursion
• From: Roger Bagula <rlbagulatftn at yahoo.com>
• Date: Sat, 19 Nov 2005 23:18:37 -0500 (EST)
• References: <dln0s1$ga7$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

There is actually a lot available about the logistic map:
http://documents.wolfram.com/mathematica/Demos/SoundGallery/LogisticMap.html

logistic[n_Integer]:=Module[{f,t,x},f=Compile[{x,t},Evaluate[(3+ ) x 
(1-x)]];FoldList[f,0.223,Range[n]]]

ListPlay[logistic[8000], SampleRate ->2000]
JikaiRF at aol.com wrote:
> 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.
>