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RE: Simple Recursive Map

• To: mathgroup at smc.vnet.net
• Subject: [mg35423] RE: [mg35398] Simple Recursive Map
• From: "Wolf, Hartmut" <Hartmut.Wolf at t-systems.com>
• Date: Fri, 12 Jul 2002 04:28:35 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

> -----Original Message-----
> From: Reuben [mailto:reubengann at hotmail.com]
To: mathgroup at smc.vnet.net
> Sent: Thursday, July 11, 2002 11:24 AM
> Subject: [mg35423] [mg35398] Simple Recursive Map
> 
> 
> I have the map
> 
> x_n+1=y_n-a*(x_n)^2 - 1
> y_n+1=b*x_n
> 
> If I specify a,b, x_0 and y_0, how can I make Mathematica iterate
> through this numerically to give me x_50 and y_50?
> 
> Thanks
> Reuben
> 

Reuben, 

try, e.g.

In[1]:= Clear[x, y]

In[2]:= x[n_] := x[n] = y[n - 1] - a*x[n - 1]^2 - 1;
        y[n_] := y[n] = b*x[n - 1];

In[4]:= x[0] = 1; y[0] = 0; a = -.1; b = .95;

In[5]:= ListPlot[Array[x, {50}], PlotJoined -> True, PlotRange -> All]

In[6]:= << Graphics`MultipleListPlot`
In[7]:= MultipleListPlot[Transpose[Partition[Array[x, {200}], 2]], 
  SymbolShape -> Point, 
  SymbolStyle -> {{AbsolutePointSize[4], Hue[0]}, {AbsolutePointSize[4], 
        Hue[.7]}}]


Don't forget to Clear x and y (and consequentely redefine it) when changing
the parameters a, b or the initial conditions.

--
Hartmut