[R-sig-dyn-mod] ode with variable dependent on results from previous time step

[Guadalupe Peralta]

Hi Thomas.

Matrix algebra will solve my problems, thank you very much for the
suggestion. Interactions are positive for both species because they benefit
from each other, i.e. it's a mutualism.

Thanks again.



2017-02-28 3:13 GMT+13:00 Thomas Petzoldt <thomas.petzoldt at tu-dresden.de>:

> Hi,
>
> I don't yet completely understand what you want, but maybe the following
> can help you a little bit.
>
> 1) your code is not completely correct, as parms$c does not contain the
> interaction matrix. Add a print to your function to see this:
>
>     c <- params$c
>     print(c)
>
>
> 2) using for-loops in a model function is quite unusual and, together with
> calculating sums a strong indication to me, that you should consider matrix
> multiplication, see page 124 vs. 123 in our tutorial:
>
> http://desolve.r-forge.r-project.org/user2014/tutorial.pdf#124
>
> That example shows a multi-species Lotka-Volterra model. Could it be
> possible that you want something like that?
>
> 3) I wonder also, why you use c*P[i] and not c[i,j] and why all
> interactions are positive.
>
> 4) Finally: in ODE models, "time steps" are infinitesimally small (i.e.
> close to zero). This means that interaction happens instantaneously or with
> other words: all variables are a result from previous time. Time is
> continuous, so time "step" and "step before" do not make much sense --
> except the technical fact that the solver approximates continuous time with
> finite steps; or "time delay" for delay differential equations, but this
> would be another story.
>
> Regards,
>
> Thomas P.
>
>
> Am 27.02.2017 um 05:02 schrieb Guadalupe Peralta:
>
>> funcPA <- function (t, y, params, nsp) {
>>   with(as.list(c(y,params)), {
>>     nP <- nsp[1]
>>     nA <- nsp[2]
>>     ntot <- nP + nA
>>     P <- y[1:nP]
>>     A <- y[(nP + 1):ntot]
>>     dP <- array(0, nP)
>>     dA <- array(0, nA)
>>     c <- params$c
>>     for (i in 1:nP) {
>>       for (j in 1:nA){
>>         dP[i] <- P[i] + sum(c*A[j]*P[i])
>>         dP
>>         dA[j] <- A[j] + sum(c*P[i]*A[j])
>>         dA }}
>>     res <-list(c(dP, dA))
>>   })
>> }
>>
>> nsp <- c(nP=3, nA=2)
>> c <- list()
>> c[[1]] <- matrix(c(0.1,0.11,0.12,0,0,0.1),nrow=3, ncol=2)
>> y <- c(P1=2, P2=1, P3=2, A1=1, A2=2)
>>
>> ode(y=y, times=seq(0,1,by=0.1), func=funcPA, nsp=nsp, parms=c)
>>
>
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