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

• Main Author: Rech P.C.*
• Publication Date: 2019
• Format: Article
• Language: eng
• Source: Repositório Institucional da Udesc
• dARK ID: ark:/33523/001300000gvbj
• Download full: https://repositorio.udesc.br/handle/UDESC/5570

© 2018, Springer Nature Switzerland AG.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.