J Abstract Reaction Systems and Their Models

In a series of articles, Rossler proposed abstract models which exhibit increasingly complicated oscillations. Most of these reaction schemes are in three dimensions and are accompanied by rate equations in discussing the behavior of the system. 

Unlike the two dimensional systems, in three dimensional examples a number of complex solutions can be obtained. These will be illustrated by abstract models. 

Significance of these models is that the complicated solutions are shown to exist even for simple nonlinear dynamic systems. Recently some of these models have been applied to explain the oscillations in experimental systems, e.g. Olsen and Degn (1977). 

The dotted arrows indicate catalytic rate controls. The rate equations are given as follows  

In this 3-dimensional system a stable limit cycle is obtained as an oscillating solution. 

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