Re: Delay DE's

*To*: mathgroup at smc.vnet.net*Subject*: [mg48232] Re: Delay DE's*From*: sean_incali at yahoo.com (sean kim)*Date*: Wed, 19 May 2004 02:42:08 -0400 (EDT)*References*: <c89p9i$sv8$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

with NDelaySolve.m k0 = 1; k1 = 1.7; tau = 1; f = k1 x[t](1 - x[t - tau]/k0) ; tlimit = 200; sol = NDelaySolve[{x'[t] == k1 x[t](1 - x[t - tau]/k0) }, {x[t] == 0.01}, {t, 0, 200}]; Plot[Evaluate[x[t] /. sol ], {t, 0, 200}]; seems to work better than NDelayDSolve. look at your original post for the NDelaySolve code. sean Virgil Stokes <virgil.stokes at neuro.ki.se> wrote in message news:<c89p9i$sv8$1 at smc.vnet.net>... > 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