Nonlinear Sciences – Chaotic Dynamics
Scientific paper
2006-03-09
D. G. Ke, H. Zhang, Q. Y. Tong, Acta Physica Sinica 2005 54: 534
Nonlinear Sciences
Chaotic Dynamics
16 page, 8 figures,a revised English version of a article published in Chinese
Scientific paper
A new complexity measure named as Lattice Complexity is presented for finite symbolic sequences. This measure is based on the symbolic dynamics of one-dimensional iterative maps and Lempel-Ziv Complexity. To make Lattice Complexity distinguishable from Lempel-Ziv Complexity, an approach called fine-graining process is also proposed. When the control parameter fine-graining order is small enough, the two measures are almost equal. While the order increases, the difference between the two measures becomes more and more significant. Applying Lattice Complexity to logistic map with a proper order, we find that the sequences that are regarded as complex are roughly at the edges of chaotic regions. Further derived properties of the two measures concerning the fine-graining process are also discussed.
Ke Da-Guan
Tong Qin-Ye
Zhang Hong
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