  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.
