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MathGroup Archive 2004

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Re: NDSolve and time-delayed equations?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg46895] Re: [mg46750] NDSolve and time-delayed equations?
  • From: sean kim <sean_incali at yahoo.com>
  • Date: Sun, 14 Mar 2004 03:24:14 -0500 (EST)
  • Reply-to: sean_incali01 at yahoo.com
  • Sender: owner-wri-mathgroup at wolfram.com

the equation you posted is solvable in Mathematica 5.0 and i'm
not sure if it's delay equation. like...

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

the one with [t, t-lag] is a delay equation though. 

what kind of problem results in an equation as the
first? would you mind explain it? 

sean




--- Gareth Russell <gjr2008 at columbia.edu> wrote:
> 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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