Chaos in kinetic models

Two lines of research have been taken. Some people strive to construct ever more realistic (from the chemical point of view) models, starting from simple formal models, while others try to show that refined models of the Belousov-Zhabotinskii reaction are able to reproduce the apparently chaotic behaviour found in experiments. 

A to the first line, Rossler (1976) was the first to provide a chemical model of chaos. It was not a mass-action-type model, but a three-variable system with Michaelis-Menten-type kinetics. Next Schulmeister (1978) presented a three-variable Lotka-type mechanism with depot. This is a mass-action-type model. In the same year Rossler (1978) presented a combination of a Lotka-Volterra oscillator and a switch he calls the Cause switch showing chaos. This model was constructed upon the principles outlines by Rossler (1976a) and is a three-variable nonconservative model. Next Gilpin (1979) gave a complicated Lotka-Volterra-type example. Arneodo and his coworkers (1980, 1982) were able to construct simple Lotka-Volterra models in three as well as in four variables having a strange attractor. 

The most realistic reaction to provide chaos so far was presented by Willamowski Rossler (1980) at the 1979 Aachen meeting. This model may be considered as an approximation (via the introduction of external components) of a conservative, unconditionally detailed balanced reaction. The reaction is worth depicting here  

The next step should lead to the meeting point with the other line of research and should provide chemically realistic models of an actual reaction that shows irregular behaviour. Chaos in the model should be proved and understood theoretically, not just shown numerically. 

At the time of writing there is no sufficient reason to be more resolute than Ganapathisubramanian Noyes (1982) who said ... uncertainty must 

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