Deterministic Chaos

The Logistic Map

Now we incorporate the competition effect.

First, competition occurs between pairs of animals:

two fish trying to catch the same insect,

two lions trying to bring down the same wildebeest,

two catepillars trying to eat the same blade of grass,

two students competing for the only A in the class (just kidding - is anyone still reading this?).

If C stands for the competition factor, the population model becomes

P_n+1 = (1 + B - D)*P_n - C*(number of competitive pairs).

So how many competitive pairs are in a population of N animals?

For example, suppose the population consists of eight animals.

Animal 1 can compete with animal 2, with animal 3, ..., with animal 8.

Assuming no bipolar disorders in the population, animal 1 cannot compete with itself. So there are seven competitive pairs involving animal 1.

These are colored red in the chart.

What about animal 2?

Return to the Logistic Map.