Synchronization of Boolean Dynamical Systems: A Spectral Characterization

被引：0
|
作者：
Parriaux, Jeremy [1 ]
Guillot, Philippe
Millerioux, Gilles [1 ,2 ]
机构：
[1] Nancy Univ, CNRS, Res Ctr Automat Control Nancy CRAN UMR 7039, Nancy, France
[2] Univ Paris 08, LAGA, UMR 7539, F-93526 St Denis 02, France
来源：
SEQUENCES AND THEIR APPLICATIONS-SETA 2010 | 2010年 / 6338卷
关键词：
D O I：
暂无
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
In this paper a spectral characterization of the synchronization property of Boolean dynamical systems is provided. Conditions on the spectrum of the next-state function are derived for two systems coupled in a unidirectional way - also called master-slave configuration - to guarantee self-synchronization. Two kinds of self-synchronization are discussed: the statistical one and the finite one. Next, some conditions are stated for a specific input sequence to allow the system to be self-synchronizing. Some of the results are based on the notion of influence of variables, a notion that is extended to vectorial Boolean functions for the purpose of the paper. A potential application to cryptography is finally given.
引用
收藏
页码：373 / +
页数：2
相关论文
共 50 条
  • [1] Forced synchronization of autonomous dynamical Boolean networks
    Rivera-Duron, R. R.
    Campos-Canton, E.
    Campos-Canton, I.
    Gauthier, Daniel J.
    [J]. CHAOS, 2015, 25 (08)
  • [2] Synchronization of spectral components and its regularities in chaotic dynamical systems
    Hramov, AE
    Koronovskii, AA
    Kurovskaya, MK
    Moskalenko, OI
    [J]. PHYSICAL REVIEW E, 2005, 71 (05):
  • [3] Boolean monomial dynamical systems
    Colón-Reyes O.
    Laubenbacher R.
    Pareigis B.
    [J]. Annals of Combinatorics, 2005, 8 (4) : 425 - 439
  • [4] Spectral characterization of Wiener-Wintner dynamical systems
    Assani, I
    [J]. COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 2001, 332 (04): : 321 - 324
  • [5] Spectral characterization of Wiener-Wintner dynamical systems
    Assani, I
    [J]. ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2004, 24 : 347 - 365
  • [6] CONDITION (K) FOR BOOLEAN DYNAMICAL SYSTEMS
    Carlsen, Toke Meier
    Kang, Eun Ji
    [J]. JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2022, 112 (02) : 145 - 169
  • [7] On the Theory of Synchronization of Dynamical Systems
    Shchennikov, A. V.
    Shchennikov, V. N.
    [J]. DIFFERENTIAL EQUATIONS, 2018, 54 (12) : 1674 - 1678
  • [8] Discontinuous dynamical systems and synchronization
    Luo, Albert C. J.
    [J]. EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS, 2019, 228 (06): : 1383 - 1384
  • [9] Synchronization of reconstructed dynamical systems
    Voss, HU
    [J]. CHAOS, 2003, 13 (01) : 327 - 334
  • [10] Concepts of synchronization in dynamical systems
    Yang, XS
    [J]. PHYSICS LETTERS A, 1999, 260 (05) : 340 - 344
12345