Chin. Phys. B, 2021, Vol. 30(1): 010505    DOI: 10.1088/1674-1056/abb30a
 GENERAL Prev   Next

# Synchronization mechanism of clapping rhythms in mutual interacting individuals

Shi-Lan Su(苏世兰)1, Jing-Hua Xiao(肖井华)1, Wei-Qing Liu(刘维清)2,†, and Ye Wu(吴晔)3,4
1 School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China; 2 School of Science, Jiangxi University of Science and Technology, Ganzhou 341000, China; 3 Computational Communication Research Center, Beijing Normal University, Zhuhai 519087, China; 4 School of Journalism and Communication, Beijing Normal University, Beijing 100875, China
Abstract  In recent years, clapping synchronization between individuals has been widely studied as one of the typical synchronization phenomena. In this paper, we aim to reveal the synchronization mechanism of clapping interactions by observing two individuals' clapping rhythms in a series of experiments. We find that the two synchronizing clapping rhythm series exhibit long-range cross-correlations (LRCCs); that is, the interaction of clapping rhythms can be seen as a strong-anticipation process. Previous studies have demonstrated that the interactions in local timescales or global matching in statistical structures of fluctuation in long timescales can be sources of the strong-anticipation process. However, the origin of the strong anticipation process often appears elusive in many complex systems. Here, we find that the clapping synchronization process may result from the local interaction between two clapping individuals and may result from the more global coordination between two clapping individuals. We introduce two stochastic models for mutually interacting clapping individuals that generate the LRCCs and prove theoretically that the generation of clapping synchronization process needs to consider both local interaction and global matching. This study provides a statistical framework for studying the internal synchronization mechanism of other complex systems. Our theoretical model can also be applied to study the dynamics of other complex systems with the LRCCs, including finance, transportation, and climate.
Keywords:  synchronization mechanism      clapping rhythm      numerical simulation
Received:  12 July 2020      Revised:  10 August 2020      Accepted manuscript online:  27 August 2020
 PACS: 05.45.Xt (Synchronization; coupled oscillators) 05.45.Tp (Time series analysis)
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11765008, 71731002, and 11775034) and the Jiangxi Provincial Natural Science Foundation, China (Grant No. 20202ACBL201004).
Corresponding Authors:  Corresponding author. E-mail: wqliujx@gmail.com

 1 Néda Z, Ravasz E, Brechet Y, Vicsek T and Barabàsi A L Nature 403 849 2 Néda Z, Ravasz E, Vicsek T, Brechet Y and Barabàsi A L 2000 Phys. Rev. E 61 6987 3 Néda Z, Nikitin A and Vicsek T Physica A 321 238 4 Nikitin A, Néda Z and Vicsek T 2001 Phys. Rev. Lett. 87 024101 5 Horvàt S and Néda Z Physica D 256 43 6 Xenides D, Vlachos D S and Simos T E 2008 J. Stat. Mech.-Theory Exp. 2008 P07017 7 Li D, Liu K, Sun Y and Han M 2008 Sci. China Ser. F-Inf. Sci 51 449 8 Li D, Liu K, Sun Y and Han M IEEE Trans. Circuits Syst. II-Express Briefs 56 504 9 Mann R P, Faria J, Sumpter D J T and Krause J 2013 J. R. Soc. Interface 10 20130466 10 Thomson M, Murphy K and Lukeman R 2018 Sci. Rep. 8 808 11 Su S, Xiao J, Liu W and Wu Y 2020 Europhys. Lett. 129 60004 12 Dubois D M2003 Anticipatory Behavior in Adaptive Learning Systems (Vol. 2684)(Berlin, Heidelberg: Springer) pp. 110-132 13 Sivaprakasam S, Shahverdiev E M, Spencer P S and Shore K A 2001 Phys. Rev. Lett 87 154101 14 Toral R, Masoller C, Mirasso C R, Ciszak M and Calvo O 2003 Physica A 325 192 15 Podobnik B, Fu D F, Stanley H E and Ivanov P C 2007 Eur. Phys. J. B 56 47 16 Hennig H 2014 Proc. Natl. Acad. Sci. USA 111 12974 17 Podobnik B, Horvatic D, Petersen A M and Stanley H E 2009 Proc. Natl. Acad. Sci. USA 106 22079 18 Xu N, Shang P and Kamae S 2010 Nonlinear Dyn. 61 207 19 Vassoler R T and Zebende G F 2012 Physica A 391 2438 20 Deligni\eres D and Marmelat V 2014 Physica A 394 47 21 Stephen D G and Dixon J A 2011 Chaos Solitons Fractals 44 160 22 Voss H U 2000 Phys. Rev. E 61 5115 23 Stephen D G, Stepp N, Dixon J A and Turvey M T 2008 Physica A 387 5271 24 Benoit C E, Bella S D, Farrugia N, Obrig H, Mainka S and Kotz S A 2014 Front. Hum. Neurosci. 8 494 25 Thaut M H, Miltner R, Lange H W, Hurt C P and Hoemberg V 2001 Mov. Disord. 14 808 26 Delignieres D, Ramdani S, Lemoine L, Torre K, Fortes M and Ninot G 2006 J. Math. Psychol. 50 525 27 Almurad Z M H, Roume C and Deligni\eres D 2017 Hum. Mov. Sci. 54 125 28 Coey C A, Washburn A, Hassebrock J and Richardson M J 2016 Neurosci. Lett. 616 204 29 Roume C, Almurad Z M H, Scotti M, Ezzina S, Blain H and Deligni\eres D 2018 Physica A 503 1131 30 Torre K and Deligni\eres D 2008 Biol. Cybern. 99 159 31 Deligni\eres D and Marmelat V2013 Progress in Motor Control. Advances in Experimental Medicine and Biology(New York: Springer) pp. 127-148 32 Diniz A, Wijnants M L, Torre K, Barreiros J, Crato N, Bosman A M T, Hasselman F, Cox R F A, Orden G C V and Deligni\eres D 2011 Hum. Mov. Sci. 30 889 33 Peng C K, Havlin S, Stanley H E and Goldberger A L 1995 Chaos 5 82 34 Havlin S, Amaral L A N, Ashkenazy Y, Goldberger A L, Ivanov P C, Peng C K and Stanley H E 1999 Physica A 274 99 35 Mates J 1994 Biol. Cybern 70 463 36 Jiong R and Zheng S Y 2010 Chin. Phys. B 19 070513 37 He D, Shi P and Stone L 2003 Phys. Rev. E 67 027201