dde {PBSddesolve}

Solve Delay Differential Equations

Description

A solver for systems of delay differential equations based on numerical routines from C source code solv95 by Simon Wood. This solver is also capable of solving systems of ordinary differential equations.

Usage

dde(y, times, func, parms=NULL, switchfunc=NULL, mapfunc=NULL, 
   tol=1e-08, dt=0.1, hbsize=10000) 

Arguments

y

numeric – vector of initial values of the DDE system. The size of the supplied vector determines the number of variables in the system.

times

numeric – vector of specific times to solve.

func

function – a user-supplied function that computes the gradients in the DDE system at time t. The function must be defined using the arguments: (t,y) or (t,y,parms), where t is the current time in the integration, y is a vector of the current estimated variables of the DDE system, and parms is any R object representing additional parameters (optional).
The argument func must return one of the two following return types:
1) a vector containing the calculated gradients for each variable; or
2) a list with two elements - the first a vector of calculated gradients, the second a vector (possibly named) of values for a variable specified by the user at each point in the integration.

parms

list – any constant parameters to pass to func, switchfunc, and mapfunc.

switchfunc

function – an optional function that is used to manipulate state values at given times. The switch function takes the arguments (t,y) or (t,y,parms) and must return a numeric vector. The size of the vector determines the number of switches used by the model. As values of switchfunc pass through zero (from positive to negative), a corresponding call to mapfunc is made, which can then modify any state value.

mapfunc

function – if switchfunc is defined, then a map function must also be supplied with arguments (t, y, switch_id) or t, y, switch_id, parms), where t is the time, y are the current state values, switch_id is the index of the triggered switch, and parms are additional constant parameters.

tol

numeric – maximum error tolerated at each time step (as a proportion of the state variable concerned).

dt

numeric – maximum initial time step.

hbsize

numeric – history buffer size required for solving DDEs.

Details

Please see the included demos ('blowflies', 'cooling', 'icecream', 'lorenz') for examples of how to use dde.

The demos can be run two ways:

1. Using the package utils, run the command:
   demo(icecream, package="PBSddesolve", ask=FALSE)

2. Using the package PBSmodelling, run the commands:
   require(PBSmodelling); runDemos()

The latter produces a GUI that shows all demos available from locally installed packages. Choose PBSddesolve. Note that the examples are run in the temporary working environment .PBSddeEnv.

The user supplied function func can access past values (lags) of y by calling the pastvalue function. Past gradients are accessible by the pastgradient function. These functions can only be called from func and can only be passed values of t greater or equal to the start time, but less than the current time of the integration point. For example, calling pastvalue(t) is not allowed, since these values are the current values which are passed in as y.

Value

A data frame with one column for t, a column for every variable in the system, and a column for every additional value that may (or may not) have been returned by func in the second element of the list.

If the initial y values parameter was named, then the solved values column will use the same names. Otherwise y1, y2, ... will be used.

If func returned a list, with a named vector as the second element, then those names will be used as the column names. If the vector was not named, then extra1, extra2, ... will be used.

Author(s)

Alex Couture-Beil – Software Engineer, Earthly Technologies, Victoria BC

Maintainer: Rowan Haigh, Program Head – Offshore Rockfish
Pacific Biological Station (PBS), Fisheries & Oceans Canada (DFO), Nanaimo BC
locus opus: Offsite, Vancouver BC
Last modified Rd: 2024-01-04

See Also

pastvalue

Examples

##################################################
## This is just a single example of using dde.
## For more examples see demo(package="PBSddesolve")
## the demos require the package PBSmodelling
##################################################

require(PBSddesolve)
local(env=.PBSddeEnv, expr={
  #create a func to return dde gradient
  yprime <- function(t,y,parms) {
    if (t < parms$tau)
      lag <- parms$initial
    else
      lag <- pastvalue(t - parms$tau)
    y1 <- parms$a * y[1] - (y[1]^3/3) + parms$m * (lag[1] - y[1])
    y2 <- y[1] - y[2]
    return(c(y1,y2))
  }

  #define initial values and parameters
  yinit <- c(1,1)
  parms <- list(tau=3, a=2, m=-10, initial=yinit)

  # solve the dde system
  yout <- dde(y=yinit,times=seq(0,30,0.1),func=yprime,parms=parms)

  # and display the results
  plot(yout$time, yout$y1, type="l", col="red", xlab="t", ylab="y", 
    ylim=c(min(yout$y1, yout$y2), max(yout$y1, yout$y2)))
  lines(yout$time, yout$y2, col="blue")
  legend("topleft", legend = c("y1", "y2"),lwd=2, lty = 1, 
    xjust = 1, yjust = 1, col = c("red","blue"))
})