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International Conference on Computational Science and Its Applications

ICCSA 2020: Computational Science and Its Applications – ICCSA 2020 pp 889–904Cite as

Synchronization Analysis in Models of Coupled Oscillators

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12249))

Abstract

The present work deals with the analysis of the synchronization possibility in chaotic oscillators, either completely or per phase, using a coupling force among them, so they can be used in attention systems. The neural models used were Hodgkin-Huxley, Hindmarsh-Rose, Integrate-and-Fire, and Spike-Response-Model. Discrete models such as Aihara, Rulkov, Izhikevic, and Courbage-Nekorkin-Vdovin were also evaluated. The dynamical systems’ parameters were varied in the search for chaos, by analyzing trajectories and bifurcation diagrams. Then, a coupling term was added to the models to analyze synchronization in a couple, a vector, and a lattice of oscillators. Later, a lattice with variable parameters is used to simulate different biological neurons. Discrete models did not synchronize in vectors and lattices, but the continuous models were successful in all stages, including the Spike Response Model, which synchronized without the use of a coupling force, only by the synchronous time arrival of presynaptic stimuli. However, this model did not show chaotic characteristics. Finally, in the models in which the previous results were satisfactory, lattices were studied where the coupling force between neurons varied in a non-random way, forming clusters of oscillators with strong coupling to each other, and low coupling with others. The possibility of identifying the clusters was observed in the trajectories and phase differences among all neurons in the reticulum detecting where it occurred and where there was no synchronization. Also, the average execution time of the last stage showed that the fastest model is the Integrate-and-Fire.

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Authors and Affiliations

  1. São Paulo State University (UNESP), Rio Claro, SP, Brazil

    Guilherme Toso & Fabricio Breve

Authors
  1. Guilherme Toso
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  2. Fabricio Breve
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Corresponding author

Correspondence to Guilherme Toso .

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Editors and Affiliations

  1. University of Perugia, Perugia, Italy

    Osvaldo Gervasi

  2. University of Basilicata, Potenza, Potenza, Italy

    Beniamino Murgante

  3. Chair- Center of ICT/ICE, Covenant University, Ota, Nigeria

    Sanjay Misra

  4. University of Cagliari, Cagliari, Italy

    Chiara Garau

  5. University of Cagliari, Cagliari, Italy

    Ivan Blečić

  6. Clayton School of Information Technology, Monash University, Clayton, VIC, Australia

    David Taniar

  7. Department of Information Science, Kyushu Sangyo University, Fukuoka, Japan

    Bernady O. Apduhan

  8. University of Minho, Braga, Portugal

    Ana Maria A.C. Rocha

  9. Polytechnic University of Bari, Bari, Italy

    Eufemia Tarantino

  10. Polytechnic University of Bari, Bari, Italy

    Carmelo Maria Torre

  11. Department of Neurology, University of Massachusetts Medical School, Worcester, MA, USA

    Yeliz Karaca

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Toso, G., Breve, F. (2020). Synchronization Analysis in Models of Coupled Oscillators. In: Gervasi, O., et al. Computational Science and Its Applications – ICCSA 2020. ICCSA 2020. Lecture Notes in Computer Science(), vol 12249. Springer, Cham. https://doi.org/10.1007/978-3-030-58799-4_64

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  • DOI: https://doi.org/10.1007/978-3-030-58799-4_64

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-58798-7

  • Online ISBN: 978-3-030-58799-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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