Consider the dynamical system
Is the function R(p) continuous?
Is the function
f(p) = R(p) p continuous? Notice that p(n +1) = f(p(n)).
This dynamical system might describe the population growth in a particular habitat for a particular species that hunts in packs or that cooperates in some other way. Suppose that we are interested in how the longterm population of this species depends on the initial population.
To study this we define a new function by
L(x) = Lim p(n)
n --> oo
when p(1) = x.
Draw a graph of the function L(x) and discuss whether or not it has any discontinuies.