[R] How to solve differential equations with a delay (time lag)?

Setzer.Woodrow at epamail.epa.gov Setzer.Woodrow at epamail.epa.gov
Wed Nov 29 23:26:12 CET 2006

lsoda does not solve delay differential equations, which is what you
need to be able to do.  A quick search on netlib (netlib.org) turned up
one match for "delay differential equations": ode/ddverk.f, which might
help (though not in R).

R. Woodrow Setzer, Ph. D.
National Center for Computational Toxicology
US Environmental Protection Agency
Mail Drop B205-01/US EPA/RTP, NC 27711
Ph: (919) 541-0128    Fax: (919) 541-1194

             Ravi Varadhan                                              
             <rvaradhan at jhmi.                                           
             edu>                                                    To 
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                                      [R] How to solve differential     
             11/29/2006 04:44         equations with a delay (time      
             PM                       lag)?                             


I would like to solve a system of coupled ordinary differential
where there is a delay (time lag) term.  I would like to use the "lsoda"
function "odesolve" package.  However, I am not sure how to specify the
delay term using the syntax allowed by odesolve.

Here is an example of the kind of problem that I am trying to solve:

> library(odesolve)

yprime <- function(t, y, p) {  # this function

yd1 <- p["k1"] *(t <= p["T"]) - p["k2"] * y[2]

yd2 <- p["k3"] * y[1](t - p["delay"]) - p["k4"] * y[2]  # this is not
syntactically valid, but it is what I would like to do



times <- seq(0,30,by=0.1)

y0 <- c(0,0)

parms <- c(k1=0.7, k2=0.5, k3=0.2, k4=0.8, T=10, delay=5)

Is there a way to incorporate delay in odesolve?

Any hints would be much appreciated.




Ravi Varadhan, Ph.D.

Assistant Professor, The Center on Aging and Health

Division of Geriatric Medicine and Gerontology

Johns Hopkins University

Ph: (410) 502-2619

Fax: (410) 614-9625

Email: rvaradhan at jhmi.edu




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