Using deSolve-Package to solve Euler integration

Question

I am working through the "Practical Guide to Ecological Modeling" by Soetaert and Herman. I arrived at chapter 6 ( Download ) with the example "6.7.2 Numerical Solution of a Nutrient-Algae Chemostat Model - Euler Integration". So I tried to replicate the modelling with R using the deSolve-package and the documentation . I worked through the first part and derived the following code:

require(deSolve)

# Setting parameter values
parameters <- c(Nin=10, pmax=1, ks=1, dil=0.24)

# Setting state variable values
state <- c(DIN=0.1, Phyto=1)

# Defining function
Lorenz<-function(t, state, parameters) {
  with(as.list(c(state, parameters)),{
    # Rate of change
    dDIN <- -pmax * (DIN/DIN+ks) * Phyto - dil * (DIN-Nin)
    dPhyto <- pmax * (DIN/DIN+ks) * Phyto - dil * Phyto

    # Return the rate of change
    return(list(c(dDIN, dPhyto)))
  })
}

# Define time frame
times<-seq(0,20,by=0.1)

# Solving equations
out<-ode(y=state,times=times,func=Lorenz,parms=parameters,method="euler")
head(out)

# Plotting results
par(mfrow=c(1,3), oma = c(0, 0, 3, 0))
plot(out, xlab = "time", ylab = "-")
plot(out[, "Phyto"], out[, "DIN"], pch = ".")
mtext(outer = TRUE, side = 3, "Lorenz model", cex = 1.5)

So I get no error, but I know as a fact that this solution is wrong. When I use the example code of the documentation everything works. My idea was that the error is within the defining function part. It seems strange not to include a time step operation as ...[i+1]... but the documentation works without them.

Does anybody have any experience with deSolve or the exercise as a whole and can get me any tips how to tackle the problem?

Answer 1

Your error are wrong set brackets, you have to use this:

dDIN <- -pmax * DIN/(DIN+ks) * Phyto - dil * (DIN-Nin)
dPhyto <- pmax * DIN/(DIN+ks) * Phyto - dil * Phyto

I think it´s clear why, isn´t it?