I'm currently studying population growth models in Math class right now and is presented with different equations for different models.
I think I understand that we use $dP/dt = rP$ (where $r$ is the intrinsic growth rate and $P$ is the population) when we have infinite growth.
However, I'm struggling to find the difference between the models:
$dP/dt = rP(1-P/k)$ –> (where $r$ is the intrinsic growth rate, $P$ is the population and $k$ is the carrying capacity)
and
$dP/dt = r(k-P)$ –>(where $r$ is the intrinsic growth rate, $P$ is the population and $k$ is the carrying capacity)
as they both pertain to rate of growth with carrying capacity…
Any explanation/clarification is greatly appreciated!
Best Answer
The logistic model$$dP/dt = rP(1-P/k)$$ has two equilibrium points namely $P=0$ and $P=k$ with $P=k$ being the stable one.
The $$ dP/dt = r(k-P)$$ model has only one equilibrium point which is stable at $P=k$
The behavior at $P<0$ is significantly different for the two models but they behaves similar around $P=k$