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Dynamical Analysis of a Discretized System Modelling Somitogenesis

In: Trends in Biomathematics: Modeling Health Across Ecology, Social Interactions, and Cells

Author

Listed:
  • Sándor Kovács

    (Eötvös Loránd University, Department of Numerical Analysis)

  • Noémi Gyúró-Magyar

    (Eötvös Loránd University)

Abstract

In this work, we analyse the dynamics of a discretized version of a continuous system modelling somitogenesis examined by Kovács et al. (Oscillations in a System Modelling Somite Formation. In: Mondaini, R.P. (ed.) Trends in Biomathematics: Stability and Oscillations in Environmental, Social, and Biological Models, pp. 237–248. Springer International Publishing (2022)). The explicit Euler scheme and a nonstandard finite difference scheme is constructed to transform the continuous-time system into the discrete-time model. Firstly, we discuss basic properties of the discrete system, such as boundedness of variables and positivity of solutions. We investigate whether the new discrete-time model shows dynamic consistency with its continuous counterpart.

Suggested Citation

  • Sándor Kovács & Noémi Gyúró-Magyar, 2025. "Dynamical Analysis of a Discretized System Modelling Somitogenesis," Springer Books, in: Rubem P. Mondaini (ed.), Trends in Biomathematics: Modeling Health Across Ecology, Social Interactions, and Cells, pages 179-198, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-97461-8_10
    DOI: 10.1007/978-3-031-97461-8_10
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