Deterministic Chaos

The Logistic Map

By now the pattern should be clear: the number of competitive pairs is

7 + 6 + 5 + 4 + 3 + 2 + 1 = 28

In general, for a population of N animals, the number of competitive pairs is

1 + 2 + ... + (N-1),

and this sum is known to equal (N - 1)*N/2. So our model of a population with competition is

P_n+1 = (1 + B - D)*P_n - C*(P_n - 1)*P_n/2.

Return to the Logistic Map.