Logistic Map

The logistic map is the recurrence relation p_t = kp_t-1(1 - p_t-1). It models populations such that p_t represents the normalized population at year t. For 0 ≤ k ≤ 1 populations eventually die off. For 1 < k ≲ 3.6 populations eventually settle down to one or a few nonzero values. For many values of k greater than about 3.6, the logistic map is chaotic.