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Emergence of Chaos and Complexity During System Growth

  • Andrzej Gecow
Part of the Understanding Complex Systems book series (UCS)

Summary

The main topic of this article is the emergence of chaos in networks describing adaptive systems.We investigate this process mainly during the system growth in dependency on network size when other parameters of the network do not change. However, we also compare the degree of chaos for different parameters and network types including random Erdős-Rényi and BA scale-free networks. We use Kauffman networks, and we follow Kauffmann using their parameters and the notion ‘chaos’ for them. However, we use more than two signal variants which we assume to be equally probable, therefore the Kauffman networks considered can become different from the Boolean networks. The terms ‘complex system’ and ‘complex network’ are commonly used but they have no common established definitions. We find that chaotic properties of networks well meet our intuition of complexity and that the appearance of chaotic features during system growth can be treated as complexity threshold. Crossing this threshold defines certain properties of system and mechanisms which create ‘structural tendencies’. These interesting phenomena, however, are described in another article in this book.

Keywords

Kauffman network Boolean network damage spreading chaos adaptive system 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Andrzej Gecow
    • 1
  1. 1.Institute of PaleobiologyPolish Academy of ScienceWarsawPoland

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