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

Chemical 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 Gyorgyi-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.

Automated summary

Chemical oscillators are open systems exhibiting periodic variations in reaction species concentration due to complex physico-chemical phenomena, leading to bistability, limit cycle attractors, spiral waves, Turing patterns, and deterministic chaos. The Belousov-Zhabotinsky reaction serves as a notable example of non-linear behavior in chemical systems, occurring in homogenous media and offering insights into more complex deriving phenomena. Models of Belousov-Zhabotinsky-type reactions under different operating conditions have been studied, focusing on stability and complex behaviors as a function of bifurcation parameters. Mathematically explaining the rise of waves and fronts, as well as the birth and evolution of chaotic ODEs system, provides valuable information for future biochemical reactions and reactor designs.