Periodicity of chaotic trajectories in realizations of finite computer precisions and its implication in chaos communications

Details Periodicity of chaotic trajectories in realizations of finite computer precisions and its implication in chaos communications Periodicity of chaotic trajectories in realizations of finite computer precisions and its implication in chaos communications

2003-09-03

arxiv.org/abs/nlin/0309005v2

Nonlinear Sciences

Chaotic Dynamics

10 pages, 3 figures, 2 tables

Scientific paper

10.1142/S0217979204025798

Fundamental problems of periodicity and transient process to periodicity of chaotic trajectories in computer realization with finite computation precision is investigated by taking single and coupled Logistic maps as examples. Empirical power law relations of the period and transient iterations with the computation precisions and the sizes of coupled systems are obtained. For each computation we always find, by randomly choosing initial conditions, a single dominant periodic trajectory which is realized with major portion of probability. These understandings are useful for possible applications of chaos, e.g., chaotic cryptography in secure communication.

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