Networks of Chaotic Elements

Kunihiko Kaneko and Ichiro Tsuda
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Kunihiko Kaneko: University of Tokyo, Department of Pure and Applied Sciences
Ichiro Tsuda: Hokkaido University, Department of Mathematics Graduate School of Science

Chapter 4 in Complex Systems: Chaos and Beyond, 2001, pp 107-161 from Springer

Abstract: Abstract As an example of the high-dimensional dynamics discussed in Chap. 1, let us consider a network of chaotic elements. In a network system many elements that can display chaotic dynamics interact with each other and evolve in time. Here we introduce the globally coupled map (GCM) as the simplest example of such a network of chaotic elements. We discuss the observed phenomena and th e universal concepts revealed therein in some detail, since the model provides us with a ‘dynamic many-to-many relationship’, ‘constructive model’, and ‘dynamics between the whole and its parts’. We believe that through the study of the GCM, we can work towards a methodology studying complex systems.

Keywords: Lyapunov Exponent; Spin Glass; Collective Dynamic; Lyapunov Spectrum; Information Cascade (search for similar items in EconPapers)
Date: 2001
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-56861-9_4

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DOI: 10.1007/978-3-642-56861-9_4

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