| ode {deSolve} | R Documentation |
Solves a system of ordinary differential equations.
ode(y, times, func, parms,
method=c("lsoda","lsode","lsodes","lsodar","vode","daspk", "euler", "rk4",
"ode23", "ode45"), ...)
y |
the initial (state) values for the ODE system, a vector. If y has a name attribute, the names will be used to label the output matrix. |
times |
time sequence for which output is wanted; the first value of times must be the initial time |
func |
either an R-function that computes the values of the derivatives in the ODE system (the model definition) at time t, or a character string giving the name of a compiled function in a dynamically loaded shared library.
If func is an R-function, it must be defined as:
yprime = func(t, y, parms,...). t is the current time point
in the integration, y is the current estimate of the variables
in the ODE system. If the initial values y has a names
attribute, the names will be available inside func. parms is
a vector or list of parameters; ... (optional) are any other arguments passed to the function.
The return value of func should be a list, whose first element is a
vector containing the derivatives of y with respect to
time, and whose next elements are global values that are required at
each point in times. |
parms |
parameters passed to func |
method |
the integrator to use, either a string ("lsoda","lsode","lsodes",
"lsodar","vode", "daspk", "euler", "rk4", "ode23" or "ode45") or a function
that performs integration, or a list of class rkMethod. |
... |
additional arguments passed to the integrator |
This is simply a wrapper around the various ode solvers.
See package vignette for information about specifying the model in compiled code.
See the selected integrator for the additional options
A matrix with up to as many rows as elements in times and as many columns as elements in y plus the number of "global" values returned
in the second element of the return from func, plus an additional column (the first) for the time value.
There will be one row for each element in times unless the integrator returns with an unrecoverable error.
If y has a names attribute, it will be used to label the columns of the output value.
The output will have the attributes istate, and rstate, two vectors with several useful elements.
The first element of istate returns the conditions under which the last call to the integrator returned. Normal is istate = 2.
If verbose = TRUE, the settings of istate and rstate will be written to the screen. See the help for the selected integrator for details.
Karline Soetaert <k.soetaert@nioo.knaw.nl>
ode.band for solving models with a banded Jacobian
ode.1D for integrating 1-D models
ode.2D for integrating 2-D models
aquaphy, ccl4model, where ode is used
lsoda, lsode, lsodes, lsodar, vode, daspk,
rk, rkMethod
#########################################
## Example1: Pred-Prey Lotka-Volterra model
#########################################
LVmod <- function(Time,State,Pars)
{
with(as.list(c(State,Pars)),
{
Ingestion <- rIng * Prey*Predator
GrowthPrey <- rGrow * Prey*(1-Prey/K)
MortPredator <- rMort * Predator
dPrey <- GrowthPrey - Ingestion
dPredator <- Ingestion*assEff -MortPredator
return(list(c( dPrey, dPredator)))
})
}
pars <- c(rIng =0.2, # /day, rate of ingestion
rGrow =1.0, # /day, growth rate of prey
rMort =0.2 , # /day, mortality rate of predator
assEff =0.5, # -, assimilation efficiency
K =10 ) # mmol/m3, carrying capacity
yini <- c(Prey=1,Predator=2)
times <- seq(0,200,by=1)
out <- as.data.frame(lsoda(func= LVmod, y=yini,
parms=pars, times=times))
matplot(out$time,out[,2:3],type="l",xlab="time",ylab="Conc",
main="Lotka-Volterra",lwd=2)
legend("topright",c("prey", "predator"),col=1:2, lty=1:2)
#########################################
## Example2: Resource-producer-consumer Lotka-Volterra model
#########################################
## Note:
## 1. parameter and state variable names made
## accessible via "with" statement
## 2. function sigimp passed as an argument (input) to model
## (see also lsoda and rk examples)
lvmodel <- function(t, x, parms, input) {
with(as.list(c(parms,x)), {
import <- input(t)
dS <- import - b*S*P + g*K #substrate
dP <- c*S*P - d*K*P #producer
dK <- e*P*K - f*K #consumer
res<-c(dS, dP, dK)
list(res)
})
}
## The parameters
parms <- c(b=0.0, c=0.1, d=0.1, e=0.1, f=0.1, g=0.0)
## vector of timesteps
times <- seq(0, 100, length=101)
## external signal with rectangle impulse
signal <- as.data.frame(list(times = times,
import = rep(0,length(times))))
signal$import[signal$times >= 10 & signal$times <=11] <- 0.2
sigimp <- approxfun(signal$times, signal$import, rule=2)
## Start values for steady state
xstart <- c(S=1, P=1, K=1)
## Solve model
out <- as.data.frame(ode(y=xstart,times= times,
func=lvmodel, parms, input =sigimp))
plot(out$P,out$K,type="l",lwd=2,xlab="producer",ylab="consumer")