| 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(ode(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")