ode {deSolve}R Documentation

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 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

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

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.

Author(s)

Karline Soetaert <k.soetaert@nioo.knaw.nl>

See Also

  • 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

    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(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")
    

    [Package deSolve version 1.1 Index]