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