# Discrete logistic equation, restricted growth model

• Horseboy

## Homework Statement

I need to write
\begin{align*} N_{k+1} = \frac{\lambda N_{k} }{1+aN_{k} } \end{align*}
in the form
\begin{align*} N_{k+1} = N_{k} + R(N_{k})N_{k} \end{align*}

As above

## The Attempt at a Solution

I know that
\begin{align*} N_{k+1} = N_{k} + R(N_{k})N_{k} \end{align*}
and that
\begin{align*} R(N_{k}) = -\frac{r}{K}N_{k}+r \end{align*}
where r is the growth rate, and K is the limiting factor.
Taking lambdaNk out the front, I get
\begin{align*} N_{k+1} = \lambda N_{k}\frac{1 }{1+aN_{k} } \end{align*}
Which looks a lot closer and simple as anything, but what am I trying to get to?

It all seems simple enough, and I can do the rest of the work required, but I'm just having trouble grasping what the equation should look like and how to get there...
This is some homework for my IT class on computer modelling, I've done 4/6 questions but having trouble on the first two, this one being the first. There are other questions to this part, but I think I can handle them if I can grasp this bit.
Any ideas? Help will be greatly appreciated :)

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