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<p>Distributed delays play an important role in biological modeling, and are often inevitable to obtain a sufficiently precise quantitative description of certain important processes. It is known from previous studies that mass-action type complex balanced chemical reaction networks (CRNs) containing distributed delays are stable. In this paper, we consider complex balanced biochemical reaction networks with distributed delays, containing a general class of reaction rates including Michaelis–Menten and Hill-type kinetics. We show that for integrable delay distributions defined on a finite time interval, there exists precisely one equilibrium in each stoichiometric compatibility class. The local stability of the equilibria is shown using a logarithmic Lyapunov–Krasovski functional. The theoretical results are demonstrated through two illustrative examples.</p>

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Stability of biochemical reaction networks with general kinetics and distributed time delays

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年10月23日

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  • Gyula Molnár,
  • Mihály A. Vághy,
  • Gábor Szederkényi

摘要

Distributed delays play an important role in biological modeling, and are often inevitable to obtain a sufficiently precise quantitative description of certain important processes. It is known from previous studies that mass-action type complex balanced chemical reaction networks (CRNs) containing distributed delays are stable. In this paper, we consider complex balanced biochemical reaction networks with distributed delays, containing a general class of reaction rates including Michaelis–Menten and Hill-type kinetics. We show that for integrable delay distributions defined on a finite time interval, there exists precisely one equilibrium in each stoichiometric compatibility class. The local stability of the equilibria is shown using a logarithmic Lyapunov–Krasovski functional. The theoretical results are demonstrated through two illustrative examples.