The Logistic Map is a model
for the growth of a singlespecies population having nonoverlapping generations
(for instance children are born in the spring and by next spring are mature and
productive  some insect populations are examples), and living in an environment
having limited resources. Limited resources enters the model as a competition
term: individuals must compete for available food. 
How do we build this model? Let P_{n} stand for the
population in generation n: 
P_{0} is the initial population, the size
of the population when we start observng it. 
P_{1} is the population in the first generation
after we start observing. 
P_{2} is the population in the second generation
after we start observing. 
and so on. 

We would like to find a relation between P_{n} and
P_{n+1}. If we find this relation, then knowing the population in any
generation we can determine the population in all successive generations. What do
we know? 
