The El Farol Bar Problem for next generation systems

Chapter 1
Chaos, Complexity and Irish
Music
1.1 Overview
There is a common misconception that complexity and chaos are synonymous.
Besides the nonlinearities that occur in both systems, the other properties those
two areas of mathematics share are disambiguity in definitions and having many
interesting and different applications.
Although a definition of chaos that everyone would accept does not exist,
almost everyone agrees to three properties a chaotic system should have: Chaos
is aperiodic long-term behaviour in a deterministic system that exhibits sensitive
dependence on initial conditions[4]. A time evolving property such as the move of
tectonic plates or planets, the temperature or any weather characteristic or even
the price movements in stock markets or dreams and emotions [5] may display
chaotic behaviour.
Chaos is often related to complexity, but does not follow from it in all cases.
Chaos might be occurring when studying phenomena as they progress in time,
but when the same phenomena are examined from a microscopic point of view
then, the interaction of the various parts of which the system is consisted creates
patterns and not ‘erratic’ chaotic behaviour. This is where complexity enters.
It is rather difficult to define complexity in mathematical terms, although
there is a measure of complexity there is no other way to give mathematical
definition. Dictionaries might be useful in this quest for defining complexity.
According to an online Dictionary by Oxford University Press, complex is an adjective
used to describe nouns which ‘are consisted of different and connected
parts’. An even more precise definition is ‘consisted of interconnected or interwoven
parts.’[6] That means, that in order to understand the behaviour of a complex
system we should understand the behaviour of each part, as well as how they interact
to form the behaviour of the whole. Our incapacity to describe the whole
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