LYAPUNOV EXPONENTS OF THE LOGISTIC MAP WITH PERIODIC FORCING

The iterative map Xn+1 = rnXn (1 - Xn) is investigated with rn changing periodically between two values A and B. Different periodicities are assumed, e.g., {rn} = {BABA ...} or {rn} = {BBABA BBABA...}. The Lyapunov exponent (a measure of average stability) is displayed with high resolution on the A-B-plane. The resulting images have aesthetically appealing self-similar structures. Furthermore, these images allow with one glimpse the identification of a number of system properties: coexistence of attractors, superstable curves, order by alternation of chaotic processes, and chaos by periodic resetting from a stable into an unstable fixed point.