Global Dynamics of the smallest Chemical Reaction System with Hopf\n Bifurcation

2011/09/23 by Hal L. Smith, Smith, Hal L.
Biochemistry, Genetics and Molecular Biology · Computer Science · Physics and Astronomy · #34C15 #34C25 #37C27 #74F25 #80A30 #Advanced Thermodynamics and Statistical Mechanics #Dynamical Systems (math.DS) #FOS: Mathematics #Gene Regulatory Network Analysis #Nonlinear Dynamics and Pattern Formation

paper · pdf · doi:10.48550/arxiv.1109.5204

openalex publication_date 2011/09/23 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28

Abstract

The global behavior of solutions is described for the smallest chemical\nreaction system that exhibits a Hopf bifurcation, discovered in citeWH1.\nThis three-dimensional system is a competitive system and a monotone cyclic\nfeedback system. The Poincar 'e-Bendixson theory extends to such systems\n citeMS,H0,HS,S and a Bendixson criterion exists to rule out periodic orbits\n citeLM.\n

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