Canard phenomenon and localization of oscillations in the Belousov–Zhabotinsky reaction with global feedback

2003 ◽  
Vol 119 (17) ◽  
pp. 8824-8832 ◽  
Author(s):  
Horacio G. Rotstein ◽  
Nancy Kopell ◽  
Anatol M. Zhabotinsky ◽  
Irving R. Epstein
Keyword(s):  
Belousov Zhabotinsky Reaction ◽  
Canard Phenomenon

Bromomalonic-acid-induced transition from trigger wave to big wave in the Belousov-Zhabotinsky reaction

2000 ◽  
Vol 61 (5) ◽  
pp. 5326-5329 ◽  
Author(s):  
Osamu Inomoto ◽  
Koji Abe ◽  
Takashi Amemiya ◽  
Tomohiko Yamaguchi ◽  
Shoichi Kai
Keyword(s):  
Bromomalonic Acid ◽  
Belousov Zhabotinsky Reaction

Analysis of reaction–diffusion waves in the ferroin-catalysed Belousov–Zhabotinsky reaction

1999 ◽  
Vol 1 (19) ◽  
pp. 4595-4599 ◽  
Author(s):  
Annette F. Taylor ◽  
Vilmos Gáspár ◽  
Barry R. Johnson ◽  
Stephen K. Scott
Keyword(s):  
Reaction Diffusion ◽  
Diffusion Waves ◽  
Belousov Zhabotinsky Reaction

scholarly journals Belousov-Zhabotinsky type reactions: the non-linear behavior of chemical systems

2021 ◽  
Author(s):  
Andrea Cassani ◽  
Alessandro Monteverde ◽  
Marco Piumetti
Keyword(s):  
Open Systems ◽  
Deterministic Chaos ◽  
General Information ◽  
Operating Conditions ◽  
Chemical Oscillators ◽  
Chemical Systems ◽  
Linear Behavior ◽  
Oscillatory Reactions ◽  
Non Linear ◽  
Belousov Zhabotinsky Reaction

AbstractChemical oscillators are open systems characterized by periodic variations of some reaction species concentration due to complex physico-chemical phenomena that may cause bistability, rise of limit cycle attractors, birth of spiral waves and Turing patterns and finally deterministic chaos. Specifically, the Belousov-Zhabotinsky reaction is a noteworthy example of non-linear behavior of chemical systems occurring in homogenous media. This reaction can take place in several variants and may offer an overview on chemical oscillators, owing to its simplicity of mathematical handling and several more complex deriving phenomena. This work provides an overview of Belousov-Zhabotinsky-type reactions, focusing on modeling under different operating conditions, from the most simple to the most widely applicable models presented during the years. In particular, the stability of simplified models as a function of bifurcation parameters is studied as causes of several complex behaviors. Rise of waves and fronts is mathematically explained as well as birth and evolution issues of the chaotic ODEs system describing the Györgyi-Field model of the Belousov-Zhabotinsky reaction. This review provides not only the general information about oscillatory reactions, but also provides the mathematical solutions in order to be used in future biochemical reactions and reactor designs.

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