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Bistability and Chaos Emergence in Spontaneous Dynamics of Astrocytic Calcium Concentration

Author

Listed:
  • Evgeniya V. Pankratova

    (Lobachevsky State University of Nizhni Novgorod, 603950 Nizhny Novgorod, Russia
    Neuroscience Research Institute, Samara State Medical University, 443099 Samara, Russia)

  • Maria S. Sinitsina

    (Lobachevsky State University of Nizhni Novgorod, 603950 Nizhny Novgorod, Russia)

  • Susanna Gordleeva

    (Lobachevsky State University of Nizhni Novgorod, 603950 Nizhny Novgorod, Russia
    Neuroscience and Cognitive Technology Laboratory, Center for Technologies in Robotics and Mechatronics Components, Innopolis University, 420500 Innopolis, Russia)

  • Victor B. Kazantsev

    (Lobachevsky State University of Nizhni Novgorod, 603950 Nizhny Novgorod, Russia
    Neuroscience Research Institute, Samara State Medical University, 443099 Samara, Russia
    Neuroscience and Cognitive Technology Laboratory, Center for Technologies in Robotics and Mechatronics Components, Innopolis University, 420500 Innopolis, Russia)

Abstract

In this work, we consider a mathematical model describing spontaneous calcium signaling in astrocytes. Based on biologically relevant principles, this model simulates experimentally observed calcium oscillations and can predict the emergence of complicated dynamics. Using analytical and numerical analysis, various attracting sets were found and investigated. Employing bifurcation theory analysis, we examined steady state solutions, bistability, simple and complicated periodic limit cycles and also chaotic attractors. We found that astrocytes possess a variety of complex dynamical modes, including chaos and multistability, that can further provide different modulations of neuronal circuits, enhancing their plasticity and flexibility.

Suggested Citation

  • Evgeniya V. Pankratova & Maria S. Sinitsina & Susanna Gordleeva & Victor B. Kazantsev, 2022. "Bistability and Chaos Emergence in Spontaneous Dynamics of Astrocytic Calcium Concentration," Mathematics, MDPI, vol. 10(8), pages 1-20, April.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:8:p:1337-:d:796105
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    References listed on IDEAS

    as
    1. Chen, Zhenyang & Chen, Fangqi, 2020. "Mixed mode oscillations induced by bi-stability and fractal basins in the FGP plate under slow parametric and resonant external excitations," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    2. Rozhnova, Maiya A. & Pankratova, Evgeniya V. & Stasenko, Sergey V. & Kazantsev, Victor B., 2021. "Bifurcation analysis of multistability and oscillation emergence in a model of brain extracellular matrix," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    3. Quanbao Ji & Min Ye & Zhouchao Wei, 2021. "Control of Chaotic Calcium Oscillations in Biological Cells," Complexity, Hindawi, vol. 2021, pages 1-7, February.
    4. Min Ye & Hongkun Zuo, 2020. "Stability Analysis of Regular and Chaotic Ca 2+ Oscillations in Astrocytes," Discrete Dynamics in Nature and Society, Hindawi, vol. 2020, pages 1-9, September.
    5. Megam Ngouonkadi, E.B. & Fotsin, H.B. & Louodop Fotso, P. & Kamdoum Tamba, V. & Cerdeira, Hilda A., 2016. "Bifurcations and multistability in the extended Hindmarsh–Rose neuronal oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 85(C), pages 151-163.
    6. An, Xinlei & Qiao, Shuai, 2021. "The hidden, period-adding, mixed-mode oscillations and control in a HR neuron under electromagnetic induction," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
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