deSolve (version 1.2-3)

ode: General Solver for Ordinary Differential Equations

Description

Solves a system of ordinary differential equations.

Usage

ode(y, times, func, parms, 
method = c("lsoda","lsode","lsodes","lsodar","vode","daspk", "euler", "rk4", 
         "ode23", "ode45"), ...)

Arguments

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

parms

parameters passed to func.

method

the integrator to use, either a string ("lsoda", "lsode", "lsodes", "lsodar", "vode", "daspk", "euler", "rk4", "ode23" or

...

additional arguments passed to the integrator.

Value

• 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.

Details

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.

See Also

• ode.bandfor solving models with a banded Jacobian,
• ode.1Dfor integrating 1-D models,
• ode.2Dfor integrating 2-D models,
• aquaphy,ccl4model, whereodeis used,
• lsoda,lsode,lsodes,lsodar,vode,daspk,
• rk,rkMethod

Examples

## =========================================
## 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")