Controlling economic? chaos

Chris Burford cburford at
Mon Mar 20 15:30:31 MST 1995

Controlling Chemical (or Economic?) Chaos

A friend of mine in our small Forum for Marxism, Philosophy and Science, who
shares an interest in the possible relevance of chaos theory and
complexity theory to the economy and to Marxist ideas, has drawn to my
attention an article in the March edition of Chemistry in Britain.

Entitled *Bringing Out the Order in Chaos* it is by Kenneth Showalter,
in fact Professor of Chemistry at West Virginia University. Acknowledge-
ments are to Valery Petrov at the same place and Stephen Scott at the
University of Leeds.

I noted the following, while bearing in mind economic parallels. Does anyone
else agree they are interesting?

"It is [now] possible to stabilise otherwise unstable states in chaotic
systems by applying feedback methods that are analogous to the clown's
balancing act. Unstable oscillatory behaviour can be stabilised with small,
controlled perturbations to the operating conditions of the system,
transforming irregular chaotic responses into regular periodic oscillations"."

Further "one of the most attractive features of the new control methods is
that they can be applied without knowing the mechanism of a system."
[We do not need to agree on whether the labour theory of value exists or

"Although control methods were developed some time ago, early methods
required an accurate model of the system so the governing equations could
be suitably modified to produce the desired stabilisation. The new feedback
methods, however, require only a means to monitor the system and access to
an operating condition that can be appropriately perturbed."

This work was initiated by Ott, Greborgi and Yorke at the University of
Maryland in 1990 using something now known as the OGY algorithm.

The author of the current paper has done further work on testing a
"map-based algorithm" on a famous oscillatory chemical reaction (BZ) first
discovered in the Soviet Union. He claims "the technique provides a means
to characterise a system experimentally that is beyond the traditional
methods of time series analysis. In addition, it allows a system to be
stabilised even when the operating conditions drift uncontrollably, as often
occurs in practice."

He observes that there are many applications, for example in stabilising
chaotic flames to increase efficiency in a wide range of applications
from coal-fired plants to rocket-booster engines, thereby implying there
is likely to be significant investment in the application of the methodology
and therefore the acceptance of the idea.

He notes that "while the homogenous chemical reaction is typically relegated
to the chemist's bench, spatio-temporal behaviour is found throughout nature
- especially in living systems."

He does not go on to mention among the possible living systems is the

Can anyone take this further?

Chris Burford.

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