R help - Feb 2012 - Logistic population growth and deSolve

Hello, I am new to R and I am having problems trying to model logistic
population growth with the deSolve package. I would like to run the model
for four populations with the same initial population and carrying capacity
but with different growth rates and put the results into a data frame. When
I run the following lines of code I get unexpected results from
"output" but
the format is more or less what I am looking for. When I run the function, I
get the results I expected but for only one time step. I haven't been able
to discern what the problem is and haven't gotten any error messages to clue
me in on where I am making a mistake. Advice would be grealty appreciated.
Thanks.

library(deSolve)
parameters = c(K=305,
               ra=0.8,
               rb=1.5,
               rc=2.1,
               rd=2.6)

state = c(Na=5,
          Nb=5,
          Nc=5,
          Nd=5)

logGrowth = function(time, state, parameters)
{
  with(as.list(c(state,parameters)),
    {
    
    dNa.dt = ra * Na * (1-(Na/K))
    dNb.dt = rb * Nb * (1-(Nb/K))
    dNc.dt = rc * Nc * (1-(Nc/K))
    dNd.dt = rd * Nd * (1-(Nd/K))
    
    return(list(c(dNa.dt, dNb.dt, dNc.dt, dNd.dt)))
    })
}

times = 1:20

output = ode(y = state, 
  			times = times, 
				func = logGrowth, 
				parms = parameters)

print(output)




logGrowth(times,state,parameters)

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Hi Thomas,

I've been out of office for a time, but maybe you are still waiting ...

As far as I see your model is a correctly implemented ODE (!!!) system 
and I don't understand what you mean with "unexpected results".

Would it be possible that your original intention was not a *continuous* 
ODE but a discrete system instead?

In this case, just use the "euler" method:


## continuous system (ordinary differential equation, ODE)
output = ode(y = state, times = times, func = logGrowth, parms = parameters)
plot(output)

## discrete system (difference equation)
output = ode(y = state, times = times, func = logGrowth, parms = 
parameters, method="euler")
plot(output)


Note also that you can write your problem more elegantly using vector 
and matrix notation.

Thomas Petzoldt