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First-order endotactic reaction networks.

Chuang Xu1

  • 1Department of Mathematics, University of Hawai'i at Mānoa, Honolulu, Hawaii, United States. chuangxu@hawaii.edu.

Journal of Mathematical Biology
|April 20, 2026
PubMed
Summary
This summary is machine-generated.

This study characterizes endotactic reaction graphs and provides a condition for higher-order networks. First-order endotactic systems exhibit unique, stable equilibria without needing Lyapunov functions.

Keywords:
Asymptotically autonomous differential equationsGlobal asymptotic stabilityMass-action systemStrongly endotactic reaction networkWeakly reversible reaction network

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Area of Science:

  • Chemical kinetics
  • Systems biology
  • Graph theory

Background:

  • Reaction networks model diverse phenomena using mass-action kinetics.
  • Mass-action systems are ODEs defined by reaction graphs.
  • Endotacticity is a graph property crucial for persistence and permanence analysis.

Purpose of the Study:

  • To characterize first-order endotactic reaction graphs.
  • To establish a sufficient condition for endotacticity in general reaction networks.
  • To analyze the global stability of mass-action systems.

Main Methods:

  • Graph theory for characterizing endotactic reaction graphs.
  • Spectral analysis of adjacency matrices for first-order endotactic graphs.
  • Stability theory for asymptotically autonomous differential equations.

Main Results:

  • Detailed characterization of first-order endotactic reaction graphs.
  • A sufficient condition for endotacticity in higher-order reaction networks.
  • Proof that first-order endotactic systems have unique, exponentially globally asymptotically stable equilibria.
  • Extension of global stability results to nonlinear ODEs without Lyapunov functions.

Conclusions:

  • The spectral properties of reaction graphs are linked to endotacticity.
  • First-order endotactic mass-action systems possess strong stability properties.
  • This work offers a new approach to proving global stability in reaction networks, applicable beyond endotactic systems.