Re: Delay DE's

• To: mathgroup at smc.vnet.net
• Subject: [mg48232] Re: Delay DE's
• From: sean_incali at yahoo.com (sean kim)
• Date: Wed, 19 May 2004 02:42:08 -0400 (EDT)
• References: <c89p9i\$sv8\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```with NDelaySolve.m

k0 = 1; k1 = 1.7; tau = 1;

f = k1 x[t](1 - x[t - tau]/k0) ;

tlimit = 200;

sol = NDelaySolve[{x'[t]  == k1 x[t](1 - x[t - tau]/k0) }, {x[t] ==
0.01}, {t, 0, 200}];

Plot[Evaluate[x[t] /. sol ], {t, 0, 200}];

seems to work better than NDelayDSolve.

look at your original post for the NDelaySolve code.

sean

Virgil Stokes <virgil.stokes at neuro.ki.se> wrote in message news:<c89p9i\$sv8\$1 at smc.vnet.net>...
> This is a followup of my earlier query on delay differential equations.
>
> The following is code that I have used to solve a simple 1st order
> non-linear delay differential equation:
>
> k0 = 1; k1 = 1.7; tau = 1;
> k1 tau
> f = k1 x[t](1 - x[t - tau]/k0)
> tlimit = 14.1;
> NDelayDSolve[{x'[t] == f}, {x -> (0.01 &)}, {t, 0, tlimit}]
>
> Indeed Mathematica 5.0.0.0 will find the correct solution (using the
> NDelayDSolve package). This is the Hutchinson-Wright equation which is
> often used in biological models. The solution when plotted with,
>
> int = x /. %[[1]]
> Plot[int[t], {t, 0, tlimit}];
>
> shows that x[t] approaches a periodic limit cycle (as it should).
> Hoppensteadt (Analysis and Simulation of Chaotic Systems,
> Springer-Verlag, 1993) has described an interesting method for
> integrating delay-differential equations and the complete solution (for
> all non-negative t) can easily be obtained with this method.
> Unfortunately, when I use NDelayDSolve to verify this result, it fails
> for values of t  > 14.1.
>
> Finally, to my question --- What can be done to "fix" NDelayDSolve to
> give a more complete solution to this problem (e.g. from t = 0 to t = 50)?
>
> --V. Stokes

```

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