       Re: replicating variables

• To: mathgroup at smc.vnet.net
• Subject: [mg43690] Re: replicating variables
• From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
• Date: Tue, 30 Sep 2003 16:42:38 -0400 (EDT)
• Organization: Universitaet Leipzig
• References: <bl8hci\$8d6\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Hi,

I hope you are able to enter the equations in the
*correct* Mathematica syntax

sol = NDSolve[{
a'[t] == a[t] (3 - 2 b[t] - a[t]),
b'[t] == b[t] (2 - a[t] - b[t]),
a == 2, b == 1}, {a[t], b[t]}, {t, 0,
20}]

ParametricPlot[Evaluate[{a[t], b[t]} /. sol[]], {t, 0, 20}]

and

ParametricPlot3D[Evaluate[{t, a[t], b[t]} /. sol[]], {t, 0, 20},
BoxRatios -> {1, 1, 1}]

Regards
Jens

Young Kim wrote:
>
> Hi,
>
>   Let's say I have two non linear differential equations which cannot be
> analytically solved,
>   for example,
>
>   a[t]' == a[t] { 3 - 2 b[t] - a[t] }
>   b[t]' == b[t] { 2 - a[t] - b[t] }
>
>   What do I need to do if I want to draw parametric curve of
>   r[t] = { a[t], b[t] }, or { a[t], b[t], t } in 3D where a[t] , b[t]
> are the numerical solutions of the preceding equations.
>   Thanks.
>
>   Young
>
>

```

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