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Input-Output Mechanism of the Discrete Chaos Extension

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Complex Motions and Chaos in Nonlinear Systems

Part of the book series: Nonlinear Systems and Complexity ((NSCH,volume 15))

Abstract

In this chapter the extension of chaos in difference equations is discussed. The theoretical results are based on chaos in the sense of Devaney and a period-doubling cascade. The existence of homoclinic and heteroclinic orbits is rigorously proved, and a theoretical control technique for the extended chaos is proposed. The results are supported with the aid of simulations. Arbitrarily high-dimensional chaotic discrete-time dynamical systems can be designed by means of the presented technique. A discrete gonorrhea model is utilized to generate chaotic behavior in population dynamics.

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Acknowledgements

M.O. Fen is supported by the 2219 scholarship programme of TÃœBÄ°TAK, the Scientific and Technological Research Council of Turkey.

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Authors and Affiliations

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

    Marat Akhmet & 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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Editors and Affiliations

  1. San Luis Potosi University, San Luis Potosi, Mexico

    Valentin Afraimovich

  2. Institute of Engineering, Polytechnic of Porto, Porto, Portugal

    José António Tenreiro Machado

  3. School of Energy&PowerEngineering, Xi’an Jiaotong University, Shaanxi Province, Shaanxi, China

    Jiazhong Zhang

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Akhmet, M., Fen, M.O. (2016). Input-Output Mechanism of the Discrete Chaos Extension. In: Afraimovich, V., Machado, J., Zhang, J. (eds) Complex Motions and Chaos in Nonlinear Systems. Nonlinear Systems and Complexity, vol 15. Springer, Cham. https://doi.org/10.1007/978-3-319-28764-5_7

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  • DOI: https://doi.org/10.1007/978-3-319-28764-5_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-28762-1

  • Online ISBN: 978-3-319-28764-5

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