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Journal of Mathematical Chemistry

, Volume 57, Issue 2, pp 632–637 | Cite as

Organization of the periodicity in the parameter-space of a glycolysis discrete-time mathematical model

  • Paulo C. RechEmail author
Original Paper
  • 25 Downloads

Abstract

In this paper, we report on the dynamics of a discrete-time mathematical model, which is obtained by the forward Euler method from the continuous-time mathematical model of the glycolysis process. More specifically, here we investigate the parameter-space of a two-dimensional map resulting from this discretization process. Different places where period-doubling and Naimark–Sacker bifurcations occur are determined. We also investigate the organization of typical periodic structures embedded in a quasiperiodic region which is a result of a Naimark–Sacker bifurcation. We identify period-adding, Farey, and Fibonacci sequences of periodic structures embedded in this quasiperiodic region.

Keywords

Glycolysis process Naimark–Sacker bifurcation Period-doubling bifurcation Forward Euler method 

Notes

Acknowledgements

The author thanks Conselho Nacional de Desenvolvimento Científico e Tecnológico-CNPq, and Fundação de Amparo à Pesquisa e Inovação do Estado de Santa Catarina-FAPESC, Brazilian Agencies, for financial support.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Departamento de FísicaUniversidade do Estado de Santa CatarinaJoinvilleBrazil

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