Witnessing the quasiperiodic-ordering transition of one-dimensional k-component Fibonacci sequences

Yaqi Tao

Physica A: Statistical Mechanics and its Applications, 2017, vol. 473, issue C, 40-44

Abstract: How much disorder in sequences is a fundamental question in many fields of science. A quantity, ZL, is proposed to assess the degree of disorder (DOD) of one-dimensional k-component Fibonacci sequences, where k is an arbitrary integer and L is the sequence length. Hu et al. have proved that such sequences are quasiperiodic when k≤5, while still ordering when k>5 (Hu et al., 1993). It is numerically found that for each k, there is an inflection point in the function of ZL versus L at a certain Lk∗. On one side, ZL∝Lαk when L0 when k≥6. This result is consistent with what found by Hu et al.. Therefore, αk can be as a witness of the quasiperiodic-ordering transition in the studied sequences. On the other hand, ZL∝L2.0139 when L>Lk∗ for all k. Further, the larger the ZL, the more disordered the sequence is. For LLk∗, ZL is almost independent of k, i.e., the DOD is almost same for enough longer sequences. All these provide further understands of disorder properties in the interesting sequences.

Keywords: The degree of disorder; k-component Fibonacci sequences; Time series analysis (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437117300274
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:473:y:2017:i:c:p:40-44

DOI: 10.1016/j.physa.2017.01.020

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().