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### Jähnichen, S.; Ihle, T. and Petzoldt, T. (2008)
### Variability of microcystin cell quota: A small model explains dynamics and
### equilibria. Limnologica - Ecology and Management of Inland Waters
### 38, 339-349
`mcyst_chemostat` <-
function(){
new("odeModel",
main = function(time, init, parms) {
x <- init
with(as.list(parms), {
mu <- mu.m * x[2]/(km + x[2])
dx1 <- mu * x[1] - D * x[1] # microcystis
dx2 <- D *(S0 - x[2]) - 1/Y * mu * x[1] # substrate
dx3 <- mu * p * x[1] - (D + dM) * x[3] # mcyst
list(c(dx1, dx2, dx3))
})
},
parms = c(
mu.m = 1.08, # max. growth rate (1/d) (Long)
km = 1.61, # half sat. constant (mumol/L) (Kohl & Nicklisch)
Y = 1/1.3e-3, # Yield coefficient
S0 = 15, # phosphorus in import (umol/L)
p = 100, # mcyst production coefficient (fg/cell)
dM = 0.02, # mcyst decay coefficient (1/d) (Orr & Jones)
D = 0.8 # dilution rate of chemostat (1/d)
),
init = c(
cells = 15, # x1 in 1e6 cells/ml
phos = 15, # x2 in nmol/ml
mcyst = 0 # x3 in ng/l
),
times = c(from=0, to=100, by=1),
solver = "lsoda"
)
}
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