ilya_prigogine_isabelle_stengers_alvin_tofflerbookfi-org

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were known to mathematicians as the "attractors" of stable
systems. What is new is their application to chemical systems.
It is worth noting that the first paper dealing with instabilities
in reaction-diffusion systems was published by Thring in 1952.
In recent years new types of attractors have been identified.
They appear only when the number of independent variables
increases (there are two independent variables in the Brusselator,
the variables X and Y). In particular, we can get "strange
attractors" that do not correspond to periodic behavior.
Figure 8, which summarizes some calculations by Hao Bailin,
gives an idea of such very complicated attractor lines calculated
for a model generalizing the Brusselator through the
addition of an external periodic supply of X. What is remarkable
is that most of the possibilities we have described have
been observed in inorganic chemistry as well as in a number of
biological situations.
In inorganic chemistry the best-known example is the
Belousov-Zhabotinsky reaction discovered in the early 1960s.
The corresponding reaction scheme, the Oregonator, introduced
by Noyes and his colleagues, is in essence similar to the
Brusselator though more complex. The Belousov-Zhabotinsky
reaction consists of the oxidation of an organic acid (malonic
acid) by a potassium bromate in the presence of a suitable catalyst,
cerium, manganese, or ferroin.
INFLOW
MALONIC . ::: ...rP U ::- M :: P :