Jump to ContentJump to Main Navigation
Show Summary Details
More options …

International Journal of Nonlinear Sciences and Numerical Simulation

Editor-in-Chief: Birnir, Björn

Editorial Board: Armbruster, Dieter / Chen, Xi / Bessaih, Hakima / Chou, Tom / Grauer, Rainer / Marzocchella, Antonio / Rangarajan, Govindan / Trivisa, Konstantina / Weikard, Rudi

IMPACT FACTOR 2017: 1.162

CiteScore 2017: 1.41

SCImago Journal Rank (SJR) 2017: 0.382
Source Normalized Impact per Paper (SNIP) 2017: 0.636

Mathematical Citation Quotient (MCQ) 2017: 0.12

See all formats and pricing
More options …
Volume 19, Issue 7-8


Synchronization of Multiple Mechanical Oscillators Under Noisy Measurements Signals and Mismatch Parameters

Ricardo Aguilar-López / Juan L. Mata-Machuca
  • Corresponding author
  • Unidad Profesional Interdisciplinaria en Ingeniería y Tecnologías Avanzadas, Instituto Politécnico Nacional, 2580 IPN, DF, 07340 Mexico, Mexico
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Rafael Martínez-Guerra / Claudia A. Pérez-Pinacho
Published Online: 2018-08-23 | DOI: https://doi.org/10.1515/ijnsns-2017-0096


In this article, we present a control scheme to synchronize multiple mechanical oscillators under the master–slave configuration. The proposed scheme is applied in the synchronization of several mechanical oscillators with high nonlinear spring, where four mechanical oscillators are controlled in order to be in state of synchronization with the master mechanical oscillator against additive noise in the measurement signals and mismatch parameters. The proposed control consists of an external feedback controller with a class of hyperbolic tangent function, which gives us the possibility to overcome problems as noise in the measured output and parameter’s mismatch which is important due to the kind of control. The effectiveness of this control scheme is showed via numerical simulations with and without sustained disturbances.

Keywords: multiple coupled mechanical oscillator; master–slave configuration; parameter’s mismatch; synchronization

PACS: ®(2010); 05.45.Xt; 05.45.Gg


  • [1]

    L. M. Pecora and T. L. Carroll, Synchronization in chaotic systems, Phys. Rev. Lett. 64 (1990), 821–824.Crossref

  • [2]

    V. Afraimovich, D. Cuevas and T. Young, Sequential dynamics of master-slave systems, Dyn. Syst. 28 (2013), 154–172.Crossref

  • [3]

    S. Vaidyanathan, Analysis, properties and control of an eight-term 3-D chaotic system with an exponential nonlinearity, Int. J. Modell. Ident Control 23 (2015), 164–172.Crossref

  • [4]

    H. Liu, B. Ren, Q. Zhao and N. Li, Characterizing the optical chaos in a special type of small networks of semiconductor lasers using permutation entropy, Opt. Commun. 359 (2016), 79–84.Web of ScienceCrossref

  • [5]

    P. Chen, S. Yu and X. Zhang, ARM-embedded implementation of a video chaotic secure communication via WAN remote transmission with desirable security and frame rate, Nonlinear Dyn. 86 (2016), 725–740.Web of ScienceCrossref

  • [6]

    J. L. Mata-Machuca, R. Martínez-Guerra, R. Aguilar-López and C. Aguilar-Ibañez, A chaotic system in synchronization and secure communications, Commun. Nonlinear Sci. Numer. Simul. 17 (2012), 1706–1713.Web of Science

  • [7]

    R. Martínez-Guerra and J. L. Mata-Machuca, Generalized Synchronization via the differential primitive element, Appl. Math. Comput. 232 (2014), 848–857.Web of Science

  • [8]

    E. E. Mahmoud, Modified projective phase synchronization of chaotic complex nonlinear systems, Math. Comput. Simul. 89 (2013), 69–85.Web of ScienceCrossref

  • [9]

    Z. Odibat, A note on phase synchronization in coupled chaotic fractional order systems, Nonlinear Anal.: Real World Appl. 13 (2012), 779–789.Web of Science

  • [10]

    T. Banerjee, D. Biswas and B. C. Sarkar, Anticipatory, complete and lag synchronization of chaos and hyperchaos in a nonlinear delay-coupled time-delayed system, Nonlinear Dyn. 72 (2013), 321–332.CrossrefWeb of Science

  • [11]

    D. Dudkowski, P. Kuzma and T. Kapitaniak, Lag synchronization in coupled multistable van der Pol duffing oscillators, Discrete Dyn. Nat. Soc. 650473 (2014), 1–6.Web of Science

  • [12]

    K. Chil-Mi, R. Sunghwan, K. Won-Ho, R. Jung-Wan and P. Young-Jai, Anti-synchronization of chaotic oscillators, Phys. Lett. 320 (2003), 39–46.Crossref

  • [13]

    R. Martínez-Guerra and J. Rincon-Pasaye, Synchronization and anti-synchronization of chaotic systems: a differential and algebraic approach, Chaos Solitons Fractals 42 (2009), 840–846.CrossrefWeb of Science

  • [14]

    R. Suresh and V. Sundarapandian, Hybrid synchronization of nscroll Chua and Lure chaotic systems via backstepping control with novel feedback, Arch. Control Sci. 22 (2012), 1230–2384.

  • [15]

    K. S. Sudheer and M. Sabir, Hybrid synchronization of hyperchaotic Lu system, Pramana 73 (2009), 781–786.Crossref

  • [16]

    V. Sharma, B. B. Sharma and R. Nath, Nonlinear unknown input sliding mode observer based chaotic system synchronization and message recovery scheme with uncertainty, Chaos, Solitons Fractals 96 (2017), 51–58.Crossref

  • [17]

    C. Hua, J. Li, Y. Yang and X. Guan, Extended-state-observer-based finite-time synchronization control design of teleoperation with experimental validation, Nonlinear Dyn. 85 (2016), 317–331.CrossrefWeb of Science

  • [18]

    L. Jinhu, Y. Xinghuo and C. Guanrong, Chaos synchronization of general complex dynamical networks, Physica A. 334 (2004), 281–302.Crossref

  • [19]

    D. Li, Z. Wang and G. Ma, Controlled synchronization for complex dynamical networks with random delayed information exchanges: a non-fragile approach, Neurocomputing 171 (2016), 1047–1052.Web of ScienceCrossref

  • [20]

    W. Shen, Z. Zeng and S. Wen, Synchronization of complex dynamical network with piecewise constant argument of generalized type, Neurocomputing 173 (2016), 671–675.CrossrefWeb of Science

  • [21]

    R. Aguilar-Lopez, R. Martinez-Guerra and C. A. Perez-Pinacho, Nonlinear observer for synchronization of chaotic systems with application to secure data transmission, The European Phys. J. Spec. Top. 223 (2014), 1541–1548.Crossref

  • [22]

    C. Wang, Y. He, J. Ma and L. Huang, Parameters estimation, mixed synchronization, and antisynchronization in chaotics systems, Complexity 20 (2014), 64–73.Crossref

About the article

Received: 2017-04-26

Accepted: 2018-08-10

Published Online: 2018-08-23

Published in Print: 2018-12-19

This paper was partially supported by the Secretaría de Investigación y Posgrado of the Instituto Politécnico Nacional (SIP-IPN) under the research grant 20181591.

Conflicts of interests: The authors have declared no conflict of interest.

Citation Information: International Journal of Nonlinear Sciences and Numerical Simulation, Volume 19, Issue 7-8, Pages 699–707, ISSN (Online) 2191-0294, ISSN (Print) 1565-1339, DOI: https://doi.org/10.1515/ijnsns-2017-0096.

Export Citation

© 2018 Walter de Gruyter GmbH, Berlin/Boston.Get Permission

Comments (0)

Please log in or register to comment.
Log in