Similarity Structure and Scaling Property of the Period-Adding Phenomena

Abstract

Period-adding sequence at the locking from torus to chaos is studied with the use of a one-dimensional mapping. Similarity and various scaling properties of each cycle are found numerically, which can be explained through a “phenomenological theory” based on the existence of the fixed point function. We classify the sequence into three cases. We also apply our theory to the case in which the sequence is a window among chaotic states.