I am reading a book about modelling Complex System and on chapter 4 the following logistic growth model is presented: $$ f(x) = -\frac{a-1}{K}x+a $$ $$ x_{t} = f(x_{t-1})x_{t-1} $$ where $f(x)$ is the function that controls the growth ratio.
The book presents an exercise which says:
Create a mathematical model of population growth in which the growth ratio is highest at a certain optimal population size, but it goes down as the population deviates from the optimal size
and it suggests to use a different $f(x)$, for example an upper convex parabola that has its peak at the optimal population size $x_{op}$
Would anyone be willing to suggest me a solution?
