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Chaotification of Impulsive Systems

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Book cover Replication of Chaos in Neural Networks, Economics and Physics

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Abstract

In this chapter, we present a new method for chaos generation in non-autonomous impulsive systems. We prove the presence of chaos in the sense of Li–Yorke by implementing chaotic perturbations. An impulsive Duffing oscillator is used to show the effectiveness of our technique, and simulations that support the theoretical results are depicted. Moreover, a procedure to stabilize the unstable periodic solutions is proposed.

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Author information

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

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

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© 2016 Higher Education Press, Beijing and Springer-Verlag Berlin Heidelberg

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Akhmet, M., Fen, M.O. (2016). Chaotification of Impulsive Systems. 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_5

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  • DOI: https://doi.org/10.1007/978-3-662-47500-3_5

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-47499-0

  • Online ISBN: 978-3-662-47500-3

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