[R-sig-dyn-mod] question about the limit of conversion rate

[Jinsong Zhao]

On 2014/4/26 3:22, Thomas Petzoldt wrote:
> On 4/25/2014 8:55 PM, Jinsong Zhao wrote:
>> Hi Thomas,
>>
>> Thank you very much for the reply. "auxiliary variable" help me
>> much, so I can monitor all variable during the simulation.
>>
>> In my situation, events doesn't work, because Uc is not a state
>> variable, while I consulted the help page of events that stated that
>> "An 'event' occurs when the value of a state variable is suddenly
>> changed, e.g. because a value is added, subtracted, or multiplied."
>
>
> ... ok, then use a forcing function. The following example is
> a modified version taken from the ?rk help page.
>
>
> SPCmod <- function(t, x, parms, input)  {
>    with(as.list(c(parms, x)), {
>      import <- input(t)
>      dS <- import - b*S*P + g*C    # substrate
>      dP <- c*S*P  - d*C*P          # producer
>      dC <- e*P*C  - f*C            # consumer
>      res <-
>      list(c(dS, dP, dC), import=import)
>    })
> }
>
> parms <- c(b = 0.1, c = 0.1, d = 0.1, e = 0.1, f = 0.1, g = 0.1)
> times <- seq(0, 100, length = 501)
> xstart <- c(S = 1, P = 1, C = 1)
>
> ## forcing function: external signal with rectangle impulse
> signal <- data.frame(times  = times, import = 0)
> signal$import[signal$times >= 10 & signal$times <= 11] <- 0.2
> sigimp <- approxfun(signal$times, signal$import, rule = 2)
>
> out  <- ode(xstart, times, SPCmod, parms, hini = 0.1, input = sigimp)
> plot(out)
>
>
> Note that 'in theory' discrete events violate the assumptions of
> differential equations that are continuous systems by definition.
> Fortunately, most solvers of deSolve are quite robust and can handle
> this in practice, but pulses with smooth transitions can be faster.
>
> This was discussed last year, see the following thread in the archives:
>
> https://stat.ethz.ch/pipermail/r-sig-dynamic-models/2013q2/000214.html
>
> Hope it helps
>
> Thomas

Thank you very much! The example makes sense. I think I have understood 
how it works.

Best wishes,
Jinsong