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Synchronization of a nonlinear oscillator with a sum signal from equivalent oscillators

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  • Vieira, Robson
  • Martins, Weliton S.
  • Barreiro, Sergio
  • Oliveira, Rafael A. de
  • Chevrollier, Martine
  • Oriá, Marcos

Abstract

Coupling of chaotic oscillators has evidenced conditions where synchronization is possible, therefore a nonlinear system can be driven to a particular state through input from a similar oscillator. Here we expand this concept of control of the operational state of a nonlinear oscillator by showing that it is possible to induce nonlinear systems to follow a linear superposition of trajectories of two (or more) equivalent systems, using only partial information from them. We show that the trajectory of the receiving oscillator converges to that of the sum of the two (or more) drivers. These results are demonstrated through experimental realization in electronic circuits and numerical simulations, and analysed through calculations of transverse Lyapunov exponents. These behaviors are observed in known nonlinear systems, opening the way for improving description and control of complex systems.

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  • Vieira, Robson & Martins, Weliton S. & Barreiro, Sergio & Oliveira, Rafael A. de & Chevrollier, Martine & Oriá, Marcos, 2021. "Synchronization of a nonlinear oscillator with a sum signal from equivalent oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    • Handle: RePEc:eee:chsofr:v:153:y:2021:i:p1:s0960077921009358
    DOI: 10.1016/j.chaos.2021.111581
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    References listed on IDEAS

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    1. Carsten Schäfer & Michael G. Rosenblum & Jürgen Kurths & Hans-Henning Abel, 1998. "Heartbeat synchronized with ventilation," Nature, Nature, vol. 392(6673), pages 239-240, March.
    2. Apostolos Argyris & Dimitris Syvridis & Laurent Larger & Valerio Annovazzi-Lodi & Pere Colet & Ingo Fischer & Jordi García-Ojalvo & Claudio R. Mirasso & Luis Pesquera & K. Alan Shore, 2005. "Chaos-based communications at high bit rates using commercial fibre-optic links," Nature, Nature, vol. 438(7066), pages 343-346, November.
    3. Louis M. Pecora & Francesco Sorrentino & Aaron M. Hagerstrom & Thomas E. Murphy & Rajarshi Roy, 2014. "Cluster synchronization and isolated desynchronization in complex networks with symmetries," Nature Communications, Nature, vol. 5(1), pages 1-8, September.
    4. Michael T. SCHAUB & Neave O'CLERY & Yazan N. BILLEH & Jean-Charles DELVENNE & Renaud LAMBIOTTE & Mauricio BARAHONA, 2016. "Graph partitions and cluster synchronization in networks of oscillators," LIDAM Reprints CORE 2886, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. Steven H. Strogatz, 2001. "Exploring complex networks," Nature, Nature, vol. 410(6825), pages 268-276, March.
    6. Yu, Hongjie & Peng, Jianhua, 2006. "Chaotic synchronization and control in nonlinear-coupled Hindmarsh–Rose neural systems," Chaos, Solitons & Fractals, Elsevier, vol. 29(2), pages 342-348.
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    Cited by:

    1. Remus-Daniel Ene & Nicolina Pop, 2023. "Optimal Homotopy Asymptotic Method for an Anharmonic Oscillator: Application to the Chen System," Mathematics, MDPI, vol. 11(5), pages 1-14, February.

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