Re: Simple Recursive Map

• To: mathgroup at smc.vnet.net
• Subject: [mg35434] Re: [mg35398] Simple Recursive Map
• From: Murray Eisenberg <murraye at attbi.com>
• Date: Fri, 12 Jul 2002 04:28:53 -0400 (EDT)
• Organization: Mathematics & Statistics, Univ. of Mass./Amherst
• References: <200207110924.FAA02123@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```You program it essentially the way you said it, just converting to
Mathematica notation for everything and using n on the left-hand sides
of the recurrence relations instead of n + 1:
Clear[x, y]

x[n_] := x[n] = y[n - 1] - a x[n - 1]^2 - 1
y[n_] := y[n] = b x[n - 1]
x[0] = 1.;  y[0] = -1.; a = 0.02; b = 1/3.;

{x[49], y[49]}
{-1.57436, -0.524786}

Notice the (highly recommended) use of "caching" the values -- the
subexpressions x[n_] := x[n] = and similarly for y -- in the recurrence
relations in order to speed up the calculations.  Without that,
Mathematica doesn't "remember" the values of x and y when it calculates
them and has to re-calculate them for each subsequent evaluation.

Reuben wrote:
>
> 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

--
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street
Amherst, MA 01375

```

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