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Replication of Chaos in Neural Networks, Economics and Physics

Part of the book series: Nonlinear Physical Science ((NPS))

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Abstract

The theory of dynamical systems starts with H. Poincaré, who studied nonlinear differential equations by introducing qualitative techniques to discuss the global properties of solutions (Devaney, An Introduction to Chaotic Dynamical Systems, 1989) [1]. His discovery of the homoclinic orbits figures prominently in the studies of chaotic dynamical systems. Poincaré first encountered the presence of homoclinic orbits in the three-body problem of celestial mechanics (Andersson, Arch. Hist. Exact Sci., 48:133–147, 1994) [2].

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Authors and Affiliations

  1. Department of Mathematics, Middle East Technical University, 06800, Ankara, Turkey

    Marat Akhmet

  2. Neuroscience Institute, Georgia State University, 30303, Atlanta, GA, USA

    Mehmet Onur Fen

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  1. Marat Akhmet
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  2. Mehmet Onur Fen
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Correspondence to Marat Akhmet .

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Akhmet, M., Fen, M.O. (2016). Introduction. In: Replication of Chaos in Neural Networks, Economics and Physics. Nonlinear Physical Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-47500-3_1

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