| The Logistic Map is a model
for the growth of a single-species population having non-overlapping 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 Pn stand for the
population in generation n: |
| P0 is the initial population, the size
of the population when we start observng it. |
| P1 is the population in the first generation
after we start observing. |
| P2 is the population in the second generation
after we start observing. |
| and so on. |
|
| We would like to find a relation between Pn and
Pn+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? |
|