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Parametric perturbation in a model that describes the neuronal membrane potential

Author

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  • da Costa, Diogo Ricardo
  • Hansen, Matheus
  • Batista, Antonio Marcos

Abstract

The Rulkov mapping is a phenomenological model that simulates the changes in the neuronal membrane potential. In this work, we introduce a parametric perturbation in the Rulkov map, that can be related to an unexpected behavior, such as a malfunction of the neuronal membrane due to pathologies. The perturbed system still keeps its main characteristics, which includes periodic behavior followed by chaotic bursts. We verify the existence of a set of periodic regions, known as shrimps, embedded in chaotic attractors in the system with parametric perturbation. Some changes in the phase space, time evolution of the variables and bifurcation diagrams are observed. Finally, we show the extreming curves, which demonstrate how is the organization of the periodic regions in the parameter space.

Suggested Citation

  • da Costa, Diogo Ricardo & Hansen, Matheus & Batista, Antonio Marcos, 2019. "Parametric perturbation in a model that describes the neuronal membrane potential," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 519-525.
    • Handle: RePEc:eee:phsmap:v:515:y:2019:i:c:p:519-525
    DOI: 10.1016/j.physa.2018.09.160
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    References listed on IDEAS

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    1. Djellit Ilhem & Kara Amel, 2006. "One-dimensional and two-dimensional dynamics of cubic maps," Discrete Dynamics in Nature and Society, Hindawi, vol. 2006, pages 1-13, August.
    2. Medeiros, E.S. & de Souza, S.L.T. & Medrano-T, R.O. & Caldas, I.L., 2011. "Replicate periodic windows in the parameter space of driven oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 44(11), pages 982-989.
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    Cited by:

    1. Trobia, José & de Souza, Silvio L.T. & dos Santos, Margarete A. & Szezech, José D. & Batista, Antonio M. & Borges, Rafael R. & Pereira, Leandro da S. & Protachevicz, Paulo R. & Caldas, Iberê L. & Iaro, 2022. "On the dynamical behaviour of a glucose-insulin model," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    2. da Costa, Diogo Ricardo & Rocha, Julia G.S. & de Paiva, Luam S. & Medrano-T, Rene O., 2021. "Logistic-like and Gauss coupled maps: The born of period-adding cascades," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).

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