Re: replicating variables

• To: mathgroup at smc.vnet.net
• Subject: [mg43693] Re: [mg43683] replicating variables
• From: sean kim <sean_incali at yahoo.com>
• Date: Tue, 30 Sep 2003 16:42:42 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```this might be little more visible.

let's use a different initial conditions. now you see
something happening. i'll let yoiu decide if the
initial conditions are reasonable.

In[1]:=
nlde = {a'[t] == a[t] (3 - 2 b[t] - a[t]), b'[t] ==
b[t] (2 - a[t] - b[t])}

nldeics = Join[nlde, {a[0] == 0.001, b[0] == 1}]
sol = NDSolve[ nldeics, {a, b}, {t, 0, 1}]

Flatten[Evaluate[{a[t], b[t]} /. sol]]

Plot[a[t]/.sol, {t, 0,1}]
Plot[b[t]/.sol, {t, 0,1}]

ParametricPlot[Evaluate[{a[t], b[t]} /. sol], {t, 0,
1}];

--- Young Kim <kim17 at fas.harvard.edu> 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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