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Rhythm synchronization and chaotic modulation of coupled Van der Pol oscillators in a model for the heartbeat

Author

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  • dos Santos, Angela M.
  • Lopes, Sergio R.
  • Viana, R.L.Ricardo L.

Abstract

We investigate a phenomenological model for the heartbeat consisting of two coupled Van der Pol oscillators. The coupling between these nodes can be both unidirectional or bidirectional, and an external driving produced by a pacemaker is also included in this model. In order to warrant a robust operation, it is desirable that both units oscillate in a synchronized way, even though in the presence of external influences or parameter mismatches which are unavoidable in a physiological setting. We study the synchronization properties of such an association with respect to the nature and intensity of coupling. We analyze in particular the (generalized) synchronization of rhythms characterized by a chaotic modulation of the oscillator frequencies. We also investigate the shadowing breakdown of numerically generated chaotic trajectories of the coupled oscillator system via unstable dimension variability in its chaotic invariant set.

Suggested Citation

  • dos Santos, Angela M. & Lopes, Sergio R. & Viana, R.L.Ricardo L., 2004. "Rhythm synchronization and chaotic modulation of coupled Van der Pol oscillators in a model for the heartbeat," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 338(3), pages 335-355.
    • Handle: RePEc:eee:phsmap:v:338:y:2004:i:3:p:335-355
    DOI: 10.1016/j.physa.2004.02.058
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    Citations

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    Cited by:

    1. Lounis, Fatima & Boukabou, Abdelkrim & Soukkou, Ammar, 2020. "Implementing high-order chaos control scheme for cardiac conduction model with pathological rhythms," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    2. Ge, Zheng-Ming & Hsu, Mao-Yuan, 2008. "Chaos excited chaos synchronizations of integral and fractional order generalized van der Pol systems," Chaos, Solitons & Fractals, Elsevier, vol. 36(3), pages 592-604.
    3. dos Santos, A.M. & Lopes, S.R. & Viana, R.L., 2008. "Synchronization regimes for two coupled noisy Liénard-type driven oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 36(4), pages 901-910.
    4. Acosta, A. & Gallo, R. & García, P. & Peluffo-Ordóñez, D., 2023. "Positive invariant regions for a modified Van Der Pol equation modeling heart action," Applied Mathematics and Computation, Elsevier, vol. 442(C).
    5. Gois, Sandra R.F.S.M. & Savi, Marcelo A., 2009. "An analysis of heart rhythm dynamics using a three-coupled oscillator model," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2553-2565.
    6. Luo, Tianjiao, 2019. "Stabilization of multi-group models with multiple dispersal and stochastic perturbation via feedback control based on discrete-time state observations," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 396-410.
    7. Ferreira, Bianca Borem & de Paula, Aline Souza & Savi, Marcelo Amorim, 2011. "Chaos control applied to heart rhythm dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 44(8), pages 587-599.
    8. Ge, Zheng-Ming & Hsu, Mao-Yuan, 2007. "Chaos in a generalized van der Pol system and in its fractional order system," Chaos, Solitons & Fractals, Elsevier, vol. 33(5), pages 1711-1745.

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