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###############################################
## Soetaert and Herman (2008) ##
## A practical guide to ecological modelling ##
## Chapter 3. ##
## Spatial components and transport ##
## Chapter 3.6.1. ##
## Autocatalysis in a flow-through ##
## stirred tank ##
###############################################
# the model
autocatalysis <- function(t,state,pars)
{
with (as.list(c(state,pars)),
{
dA <- dr*(Ain-A)-k*A*B
dB <- dr*(Bin-B)+k*A*B
dC <- -dr*C +k*A*B
return (list(c(dA,dB,dC)))
})
}
# model application
times <- seq(0,300,1)
state <- c(A=1,B=1,C=0)
parms <- c(Ain =1,Bin = 0.1, k = 0.05, dr = 0.05)
require(deSolve)
out <- as.data.frame(ode(state,times,autocatalysis,parms))
ylim <- range(c(out$A,out$B,out$C))
plot(out$time,out$A,xlab="time",ylab="concentration",
lwd=2,type="l",ylim=ylim,main="autocatalysis")
lines(out$time,out$B,lwd=2,lty=2)
lines(out$time,out$C,lwd=2,lty=3)
legend("topright",c("A","B","C"),lwd=2,lty=c(1,2,3))
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