Existence and uniqueness of periodic orbits in the cubic autocatalator

Holmes C.A. (1992) Existence and uniqueness of periodic orbits in the cubic autocatalator. Dynamics and Stability of Systems, 7 3: 163-171. doi:10.1080/02681119208806134


Author Holmes C.A.
Title Existence and uniqueness of periodic orbits in the cubic autocatalator
Journal name Dynamics and Stability of Systems
ISSN 1465-3389
Publication date 1992-01-01
Sub-type Article (original research)
DOI 10.1080/02681119208806134
Open Access Status Not yet assessed
Volume 7
Issue 3
Start page 163
End page 171
Total pages 9
Subject 2200 Engineering
Abstract Periodic orbits are sought in a mathematical model of a simple prototype chemical reaction involving essentially only two reacting species. Physically, these periodic orbits correspond to time-periodic oscillations in the concentrations of the two chemicals. Using the results for the existence and uniqueness of periodic orbits for Lienard systems, necessary and sufficient conditions are obtained for the existence of exactly one periodic orbit and of no periodic orbits. The results apply to a closed system where the quadratic autocatalytic reaction and decay step are present but the uncatalysed reaction is not and where there is only one physically relevant equilibrium solution.
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Unknown

Document type: Journal Article
Sub-type: Article (original research)
Collection: Scopus Import - Archived
 
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Created: Tue, 14 Jun 2016, 12:58:25 EST by System User