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