Thanks, now that you say its look like so easy. I dont know how i couldnt
figure out the link about these things.
Thanks again for the attention in such basic issue.
I'll keep studying, hope i can came back when get stuck again ^^

Best wishes
Augusto Ribas
2011/2/26 Thomas Petzoldt <Thomas.Petzoldt@tu-dresden.de>

> Hello Augustos,
>
> there is nothing wrong with your examples or with the used packages, at
> least not in a technical sense. The problem is indeed your mathematical
> understanding. Your observation simply shows the difference between the
> discrete (function logistico) and a continuous solution (function Logistic
> with ode).
>
> As an example, you may compare an animal population that reproduces once a
> year (= discrete) with a bacterial population with millions of individuals
> that seem to reproduce continuously. The discrete model is also called a
> "difference equation" and the continuous form a "differential equation".
> Package deSolve is intended for solving differential equations, and it can
> be also used for difference equations by using the "euler" method.
>
> Read sections 1.4, 3.1 and 3.2 of Henry Stevens book for the details.
>
> A few additional comments are interspersed below.
>
>
>
> On 2/25/2011 4:53 PM, Augusto Ribas wrote:
>
>> Hello.
>> I'm a ecology grad student in brazil.
>> Well i'm trying to figure out how to use the function ode.
>> I read the manual on pack page and tryed to copy the example to solve de
>> logistc growth model to test if it work(work i mean i understood ^^) but i
>> cant make it right.
>> Then i got to this maillist by the pack page.
>>
>> So first i solved with a  function:
>>
>> logistico<- function(k,r,N0,t){
>>  N<-c(N0,numeric(t))
>>  for(i in 1:t) N[i+1]<-{
>>  N[i] + r * N[i] * (1 - N[i]/k)
>>  }
>>  return(N)
>>  }
>>
>> then i get the results for a k=100 and r=1 in 20 times starting with a pop
>> of 2 individuals
>>
>> Nts<- logistico(100,1,2,20)
>>
>> to here its ok to me
>> now i tryed to make a function to use with desolve as following:
>>
>> Logistic<-function(t, state, parameters) {
>>  with(as.list(c(state, parameters)),{
>>  dN<- r*n*(1-n/k)
>>  list(c(dN))
>>  })
>>  }
>>
>> then tryed to solve
>>
>> library(desolve)
>>
>
> Please respect capitalization, i.e. library(deSolve)
>
>
> parameters<- c(r = 1, k = 100)
>> state<- c(n = 2)
>> times<-seq(0,20,by=1)
>> out<- ode(y = state, times = times, func = Logistic, parms = parameters)
>>
>> but the results are different
>>
>
> this is natural, because Nts contains a discrete and out a continuous
> solution. Try the following for a discrete solution with deSolve:
>
> out<- ode(y = state, times = times, func = Logistic, parms = parameters,
> method="euler")
>
> And don't forget to consult the book of Stevens and a book about
> differential calculus to understand the difference.
>
>
> out<-cbind(out,Nts)
>> matplot(x=out[,1],y=out[,2:3],xlab=c("Times"),ylab=c("Pop. Density"),
>> type="l")
>> legend(x=15,y=90,legend=c("Desolve","Function"),pch =19, col=c(1, 2))
>>
>>
>> On the book Primer of ecology with R Stevens use desolve on levins
>> metapopulation model a little bit different, takeing out the state on
>> function like...
>>
>> Logistic<-function(t, state, parameters) {
>> n<-state[1]   #<-------------------------------why this?
>>  with(as.list(parameters),{
>>  dn<- r*n*(1-n/k)
>>  return(list(dn))
>>  })
>>  }
>>
>
> In programming there are always different ways to do the same thing. Both
> methods are intended to unpack the content of "state" and "parameters" so
> that their content can be used by their names (e.g. r, n, k).
>
> While the first form:
>
> with(as.list(c(state, parameters)), .....
>
> unpacks both using the "with" function, the second form uses:
>
> n<-state[1]
>
> to "unpack" the state and
>
> with(as.list(parameters), ......
>
> to unpack the parameters. Both have their pros and cons if used for bigger
> models, and the use of either the one or the other for the logistic is only
> a matter of style.
>
> Hope it helps
>
> ThPe
>
> --
> ---------------------------------------------
> Dr. Thomas Petzoldt
> Technische Universitaet Dresden
> Faculty of Forest, Geo and Hydro Sciences
> Institute of Hydrobiology
> 01062 Dresden, Germany
>
> E-Mail: thomas.petzoldt@tu-dresden.de
> http://tu-dresden.de/Members/thomas.petzoldt
> ---------------------------------------------
>



-- 
Grato
Augusto C. A. Ribas

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