Alex Klimenko (University of Queensland, Australia)
Abstract. It is well known that many (if not most) complex systems, which can belong to seemingly unrelated fields of knowledge (e.g. technological development, biological systems, economics, history, etc), display cyclic behaviors. While the underlying physical reasons for the existence of these cycles might be different, it seems that many of the cycles have a number of common features. Could there be a common explanation for this “phenomenon of cycles”? Would it be possible to omit less significant details and find a common framework that can explain the principal mechanism that enacts cycles of this kind?
One may note that the systems referred to in the first paragraph indeed have something in common – they involve competition. This presentation introduces a framework, which can be called “complex competitive systems,” as one of the possible answers to the questions posed above. These systems involve elements that compete according to preset rules that determine winners and losers among competitors. This framework is not to be confused with game theory: the elements are not intelligent and do not select competition strategies but, instead, possess strategies determined by the elements’ properties.
The patterns of behavior of competitive systems depend on the transitivity of the competition rules. If the rules are transitive, competitive systems behave in a relatively predictable manner that can be characterized by a kind of competitive thermodynamics. Cycles are impossible for such systems. If the rules are intransitive, complex patterns of behavior involving competitive cooperations, competitive degradations and cycles can emerge. In simple terms, transitive rules correspond to the existence of a linear classification such as bad/average/good while intransitive rules allow only for relative comparisons. What may seem to be an improvement in an intransitive system may, in due course, become fatal for its survival. General properties and specific examples of transitive and intransitive systems will be discussed in the talk.