Global dynamics of the smallest chemical reaction system with Hopf bifurcation

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Abstract

The global behavior of solutions is described for the smallest chemical reaction system that exhibits a Hopf bifurcation, discovered in [12]. This three-dimensional system is a competitive system and a monotone cyclic feedback system. The Poincaré-Bendixson theory extends to such systems [2,3,6,8] and a Bendixson criterion exists to rule out periodic orbits [4].

Original languageEnglish (US)
Pages (from-to)989-995
Number of pages7
JournalJournal of Mathematical Chemistry
Volume50
Issue number4
DOIs
StatePublished - Apr 1 2012

Keywords

  • Bendixson criterion
  • Compact attractor
  • Competitive system
  • Monotone cyclic feedback system
  • Periodic orbit
  • Uniform persistence

ASJC Scopus subject areas

  • Chemistry(all)
  • Applied Mathematics

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