Delay DE's

*To*: mathgroup at smc.vnet.net*Subject*: [mg48180] Delay DE's*From*: Virgil Stokes <virgil.stokes at neuro.ki.se>*Date*: Mon, 17 May 2004 03:21:48 -0400 (EDT)*Organization*: Karolinska Institute*Sender*: owner-wri-mathgroup at wolfram.com

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