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<p>In this paper, the Michaelis–Menten dynamics are studied by reducing the original system to a new set of two nonlinear ordinary differential equations obtained via conservation relations and variable transformations. A stability analysis of the reduced system reveals the existence of a stable equilibrium point. The properties of boundedness, positivity, existence, and uniqueness of the solutions are established by constructing two sequences, which are subsequently proven to be Cauchy sequences. Finally, numerical simulations are performed to validate the theoretical results and illustrate the expected behavior of the model.</p>

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Mathematical modeling and analysis for Michaelis–Menten kinetics

  • 期刊论文

  • 发表日期：

    2025年7月11日

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  • Gülnihal Meral,
  • Derya Altıntan

摘要

In this paper, the Michaelis–Menten dynamics are studied by reducing the original system to a new set of two nonlinear ordinary differential equations obtained via conservation relations and variable transformations. A stability analysis of the reduced system reveals the existence of a stable equilibrium point. The properties of boundedness, positivity, existence, and uniqueness of the solutions are established by constructing two sequences, which are subsequently proven to be Cauchy sequences. Finally, numerical simulations are performed to validate the theoretical results and illustrate the expected behavior of the model.