Global Dynamics of the smallest Chemical Reaction System with Hopf Bifurcation
Hal L. Smith
TL;DR
This paper analyzes the global behavior of the simplest chemical reaction system exhibiting a Hopf bifurcation, extending classical theories to understand its dynamics.
Contribution
It characterizes the global dynamics of a minimal three-dimensional chemical system with Hopf bifurcation, applying and extending Poincaré-Bendixson theory and Bendixson criteria.
Findings
Describes the global behavior of the system
Extends Poincaré-Bendixson theory to this class of systems
Provides criteria to rule out periodic orbits
Abstract
The global behavior of solutions is described for the smallest chemical reaction system that exhibits a Hopf bifurcation, discovered in \cite{WH1}. This three-dimensional system is a competitive system and a monotone cyclic feedback system. The Poincar\'e-Bendixson theory extends to such systems \cite{MS,H0,HS,S} and a Bendixson criterion exists to rule out periodic orbits \cite{LM}.
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Taxonomy
TopicsNonlinear Dynamics and Pattern Formation · Gene Regulatory Network Analysis · Advanced Thermodynamics and Statistical Mechanics