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MathGroup Archive 2004

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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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