Complexity

Theories of complexity deal with systems which are usually not possible to be described using classical techniques based on equilibria and systems which are conservative and time-reversible. Complexity provides techniques to describe systems which exhibit dissipative, time dependent and emergent properties, under transition and non-equilibrium conditions. An example of a case where complexity theory is required to describe a system which does not converge to equilibrium but remains far from equilibrium is given below.

Belousov-Zhabotinsky (B-Z) reaction

Classically, chemical reactions tend to a (possibly dynamic) equilibrium over time where all constituents reach fixed concentrations within a given environment (temperature, pressure etc.). In the B-Z reaction1) 2), the concentrations of reagants oscillate in a given environment as demonstrated in the time-lapse video below. Helpfully for an example, Ce4+ ions give a yellow/orange colour to the mixture, while Ce3+ make the mixture colourless allowing visual observation of the oscillating concentrations of these ions.

Complex Adaptive Systems

Within Complexity, a class of systems known as Complex Adaptive Systems have emerged. These broadly denote systems whose constituents adapt over time in a non-reversible fashion. In general, whilst there is no common and comprehensive definition of a Complex Adaptive System (CAS), there are characteristics of systems which are often cited as criteria that are required to describe a system as Complex and Adaptive:

  • Irreversability – the system’s history may not be reversed
  • Irreducibility – the system under investigation must be considered as a whole and cannot be reduced to more simple sub-components which can be studied separately
  • Emergence – order is not predetermined and therefore system states and patterns emerge
  • Chaotic – the outputs of a model are heavily influenced by small changes in the input characteristics (e.g. the sensitive dependence on initial conditions which became known as the often quoted “butterfly effect”)
1) B. P. Belousov. Периодически действующая реакция и ее механизм. [A periodic reaction and its mechanism]. Сборник рефератов по радиационной медицине (Compilation of Abstracts on Radiation Medicine), 147:145, 1959.
2) A. M. Zhabotinsky. Периодический процесс окисления малоновой кислоты растворе (исследование кинетики реакции Белоусова). [Periodic processes of malonic acid oxidation in a liquid phase.] Биофизика [Biofizika], 9:306–311, 1964.
 
examples/complexity.txt · Last modified: 20/07/2010 11:21 by cascade     Back to top

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