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Complex Systems

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The understanding of complex systems refutes the bottom-up approach of traditional science.

The latter assumes that the underlying mechanisms of a system's behavior can be understood by studying the system's parts independently.

A complex system, however, is more than the sum of its parts. Its behavior comes about through interaction between the constituent parts.

Although the term "complex system" has multiple usages, some generally agreed upon properties of a complex system are:

  • Multiplicity of many parts, out of whose interaction "emerges" behaviour not present in the parts alone
  • Coupling to an environment with which information, energy, or other types of resources are exchanged
  • Presence of both order and randomness in (spatial) structure or (temporal) behaviour
  • Absence of a central control element, either internal or external
  • Robustness of structure and/or behaviour against significant perturbation
  • Presence of memory and feedback; enabling adaptability according to its history or feedback

The study of these systems requires a combination of methods from more than one discipline as well as the development of new mathematical and computational tools.

Complexity theory and the internet

Internet connectivity map. Image created by Matt Grint and available under Creative Commons Attribution 2.5 License

This image represents connectivity in a portion of the internet. Very small changes in one part of the network, such as infection from a virus or worm, can have huge ramifications in the network as a whole.

However, the influence of network parameters is not smooth or linear; rather, there appear to be phase transitions, like the change from ice to liquid water. The mathematics of complexity is required to find out what those transition points are.

We are part of the Bristol Centre for Complexity Sciences, an interdisciplinary doctoral training and research centre. In the Mathematics department we are interested in all theoretical aspects of complex systems including the dynamics of networks, information processing, statistical inference and quantum effects.