Lyapunov exponents of the logistic map with periodic forcing |
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Authors: | Mario Markus Benno Hess |
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Affiliation: | Max-Planck-Institut für Ernährungsphysiologie, Rheinlanddamm 201, D-4600, Dortmund 1, FRG |
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Abstract: | 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. |
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