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<p>Controlling complex reaction networks is a fundamental challenge in the fields of physics, chemistry, biology, and systems engineering. However, theories for the controllability of such nonlinear systems are yet under development. Here, we prove a general principle for catalytically-controlled reaction systems with kinetics where the reaction order and the stoichiometric coefficient match: the local stabilizability of a given state implies global controllability within its stoichiometric compatibility class. In other words, if a target state can be maintained against small perturbations by a catalytic control, the system can be catalytically controlled from any initial condition to that state. This result highlights a tight link between the local and global dynamics of nonlinear chemical reaction systems, and a&#xa0;clear relationship between controllability and thermodynamic consistency of the reaction systems. The findings illuminate the robustness of biochemical systems and offer a way to control catalytic reaction systems in a generic framework.</p>

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Local stabilizability implies global controllability in catalytically-controlled reaction networks

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月8日

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  • Yusuke Himeoka,
  • Shuhei A. Horiguchi,
  • Naoto Shiraishi,
  • Fangzhou Xiao,
  • Tetsuya J. Kobayashi

摘要

Controlling complex reaction networks is a fundamental challenge in the fields of physics, chemistry, biology, and systems engineering. However, theories for the controllability of such nonlinear systems are yet under development. Here, we prove a general principle for catalytically-controlled reaction systems with kinetics where the reaction order and the stoichiometric coefficient match: the local stabilizability of a given state implies global controllability within its stoichiometric compatibility class. In other words, if a target state can be maintained against small perturbations by a catalytic control, the system can be catalytically controlled from any initial condition to that state. This result highlights a tight link between the local and global dynamics of nonlinear chemical reaction systems, and a clear relationship between controllability and thermodynamic consistency of the reaction systems. The findings illuminate the robustness of biochemical systems and offer a way to control catalytic reaction systems in a generic framework.