Abstract
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 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.
Highlights
1.1 Historical backgroundThe first evidence of chemical oscillations dates to the early nineteenth
The review dealt with the main features of Belousov-Zhabotinsky-type reactions
Several parameters, including temperature, flowrates and concentration of chemical compounds may affect chemical oscillators occurring under dynamic conditions
Summary
The first evidence of chemical oscillations dates to the early nineteenth. These are the years of Lotka and Bray [1]. An open reactive system is controlled by kinetic laws which at a certain non-linearity degree may show strange phenomena like bistability among two steady-states [3], deeply different from the presence of a single stable thermodynamic equilibrium Entropy of these selforganizing systems seems to decrease but it is not true: even if parts of the system show this trend in time and/or space, in a general prospective they will increase their entropy [5]. Prigogine focused his attention on what he called “dissipative structures”, patterns as spiral waves and propagating fronts formed in oscillatory systems [3] This phenomenon occurs in spatially distributed media, with diffusion contributing to cause instability, and for highly non-linear systems. Chaos has been pointed out to be linked to ventricular fibrillation, occurring after a spiral wave is broken, into several others [8]
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
