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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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