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On the dynamical behaviour of a glucose-insulin model

Author

Listed:
  • 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.
  • Iarosz, Kelly C.

Abstract

Insulin is a hormone that plays a crucial role in controlling the transport of glucose from the blood to inside the cells. In the pancreas, the insulin is secreted by the β cells, according to the blood glucose concentration, and the interaction of insulin with the glucose is responsible for providing energy to the cells. In this work, we study the dynamical behaviour of a mathematical model, validated by experimental data, that considers the relationship between glucose and insulin concentrations, as well as the role of the β cells. Depending on the control parameters, the model can exhibit periodic and chaotic behaviours. Based on these behaviours, we identify complex structures in the parameter space, namely shrimp-shaped periodic windows immersed in chaotic regions. Furthermore, a parametric perturbation in the parameter related to the rate increase of insulin level secreted by cells can suppress chaos, inducing either periodic or quasi-periodic behaviour. We also investigate the structure of basins of periodic and chaotic attractors in the glucose-insulin system under parametric perturbation; the boundaries between these basins have fractal structures for some control parameters.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:155:y:2022:i:c:s0960077921011073
    DOI: 10.1016/j.chaos.2021.111753
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    References listed on IDEAS

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    1. Mendonça, J.P. & Gleria, Iram & Lyra, M.L., 2019. "Delay-induced bifurcations and chaos in a two-dimensional model for the immune response," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 517(C), pages 484-490.
    2. Ginoux, Jean-Marc & Ruskeepää, Heikki & Perc, Matjaž & Naeck, Roomila & Costanzo, Véronique Di & Bouchouicha, Moez & Fnaiech, Farhat & Sayadi, Mounir & Hamdi, Takoua, 2018. "Is type 1 diabetes a chaotic phenomenon?," Chaos, Solitons & Fractals, Elsevier, vol. 111(C), pages 198-205.
    3. Hubert, M. & Vandervieren, E., 2008. "An adjusted boxplot for skewed distributions," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5186-5201, August.
    4. Jef Huisman & Franz J. Weissing, 1999. "Biodiversity of plankton by species oscillations and chaos," Nature, Nature, vol. 402(6760), pages 407-410, November.
    5. Peixoto, Márcia L.C. & Nepomuceno, Erivelton G. & Martins, Samir A.M. & Lacerda, Márcio J., 2018. "Computation of the largest positive Lyapunov exponent using rounding mode and recursive least square algorithm," Chaos, Solitons & Fractals, Elsevier, vol. 112(C), pages 36-43.
    6. Shabestari, Payam Sadeghi & Panahi, Shirin & Hatef, Boshra & Jafari, Sajad & Sprott, Julien C., 2018. "A new chaotic model for glucose-insulin regulatory system," Chaos, Solitons & Fractals, Elsevier, vol. 112(C), pages 44-51.
    7. 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.
    8. Ferrari, F.A.S. & Viana, R.L. & Reis, A.S. & Iarosz, K.C. & Caldas, I.L. & Batista, A.M., 2018. "A network of networks model to study phase synchronization using structural connection matrix of human brain," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 496(C), pages 162-170.
    9. 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.
    10. de Souza, S.L.T. & Batista, A.M. & Baptista, M.S. & Caldas, I.L. & Balthazar, J.M., 2017. "Characterization in bi-parameter space of a non-ideal oscillator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 466(C), pages 224-231.
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