Lyapunov exponents of the logistic map with periodic forcing

Abstract The iterative map x n +1 = r n x n (1 - x n ) is investigated with r n changing periodically between two values A and B . Different periodicities are assumed, e.g. , { r n } = { BABA …} or { r n } = { 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.