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Fundamentals of Chaos Theory

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Chaos in Hydrology

Abstract

Almost all natural, physical, and socio-economic systems are inherently nonlinear. Nonlinear systems display a very broad range of characteristics. The property of “chaos” refers to the combined existence of nonlinear interdependence, determinism and order, and sensitive dependence in systems. Chaotic systems typically have a ‘random-looking’ structure. However, their determinism allows accurate predictions in the short term, although long-term predictions are not possible. Since ‘random-looking’ structures are a common encounter in numerous systems, the concepts of chaos theory have gained considerable attention in various scientific fields. This chapter discusses the fundamentals of chaos theory. First, a brief account of the definition and history of the development of chaos theory is presented. Next, several basic properties and concepts of chaotic systems are described, including attractors, bifurcations, interaction and interdependence, state phase and phase space, and fractals. Finally, four examples of chaotic dynamic systems are presented to illustrate how simple nonlinear deterministic equations can generate highly complex and random-looking structures.

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Authors and Affiliations

  1. School of Civil and Environmental Engineering, The University of New South Wales, Sydney, NSW, Australia

    Bellie Sivakumar

  2. Department of Land, Air and Water Resources, University of California, Davis, CA, USA

    Bellie Sivakumar

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  1. Bellie Sivakumar
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Sivakumar, B. (2017). Fundamentals of Chaos Theory. In: Chaos in Hydrology. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-2552-4_5

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