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<p>We provide a global analysis of the classical Brusselator system, classifying all possible configurations of equilibria, limit cycles, and nullclines. We study the infinite dynamics through the Poincaré compactification, analyze the bifurcation diagram for the finite local dynamics and draw the global phase portraits in the Poincaré disc for different ranges of the parameters. Our results extend local studies to a global perspective, yielding a complete characterization of the system’s dynamics. </p>

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Classification of Global Phase Portraits for the Brusselator System

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年6月22日

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  • Tiago M. P. de Abreu,
  • Jaume Llibre

摘要

We provide a global analysis of the classical Brusselator system, classifying all possible configurations of equilibria, limit cycles, and nullclines. We study the infinite dynamics through the Poincaré compactification, analyze the bifurcation diagram for the finite local dynamics and draw the global phase portraits in the Poincaré disc for different ranges of the parameters. Our results extend local studies to a global perspective, yielding a complete characterization of the system’s dynamics.