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MathGroup Archive 2005

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Re: Re: Recursion

  • To: mathgroup at smc.vnet.net
  • Subject: [mg62336] Re: [mg62315] Re: Recursion
  • From: Pratik Desai <pdesai1 at umbc.edu>
  • Date: Mon, 21 Nov 2005 03:54:18 -0500 (EST)
  • References: <dln0s1$ga7$1@smc.vnet.net> <200511200418.XAA28524@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Chris Chiasson wrote:

>Fujio Takata,
>
>Perhaps the following code will work for you:
>
>x[Condition[t_,t\[LessEqual]0]]=2
>x[Condition[t_,t>0]]=a x[t-1](1-x[t-1])
>Block[{a=2},Plot[x[t],{t,0,9}]]
>
>
>On another note, can anyone explain why the following code blows up?
>
>x[t_]=Piecewise[{{2,t<=0},{a x[t-1](1-x[t-1]),5>t>0}}]
>
>Regards,
>--
>http://chrischiasson.com/contact/chris_chiasson
>
>  
>
I am sorry, did not even think that you were looking for a quadriatic 
family logistic mapping

Here is my attempt for the continuous version of your system, hope this 
is what you are looking for

<< Graphics`Graphics`
Clear[a, list1, list2, y]
a = 2
y[x_] = a *x*(1 - x)
list1 = FixedPointList[y, 1]
(*Here you can change your  initial point, 1 seems to be most  
interesting so are 0.5 and 0*)
list2 = Table[{list1[[s]], list1[[s + 1]]}, {s, 1, Length[list1]}]
plot2 = ListPlot[list2, PlotStyle -> PointSize[0.02]]
plot3 = Plot[{a*x*(1 - x), x}, {x, 0, 1}]
DisplayTogether[plot2, plot3]


Hope this helps

Pratik .

-- 
Pratik Desai
Graduate Student
UMBC
Department of Mechanical Engineering
Phone: 410 455 8134



  • References:
    • Re: Recursion
      • From: "Chris Chiasson" <chris.chiasson@gmail.com>
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