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MathGroup Archive 2004

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NDSolve and time-delayed equations?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg46750] NDSolve and time-delayed equations?
  • From: Gareth Russell <gjr2008 at columbia.edu>
  • Date: Fri, 5 Mar 2004 01:47:03 -0500 (EST)
  • Organization: Columbia University
  • Sender: owner-wri-mathgroup at wolfram.com

Hi,

Can NDSolve be used to approximate the dynamics of continuous but 
time-delayed equations? Here is an example of the standard continuous 
logistic model used in ecology:

NDSolve[{n'[t] == 0.5*n[t]*(1 - n[t]/100), n[0] == 10}, n, {t, 0, 20}]

It does, of course, have an analytical solution.

A time-delayed version would make the derivative a function of two 
values: n'[t,t-lag], but I can't figure out if a formulation like this 
is possible. The key thing seems to be that while the derivative of n 
is a simple function of two parameters, n itself is not.

Any suggestions, other than iterating as a discrete-time model with 
very small time-steps?

Gareth Russell
Columbia University


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