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Recent Advances in Nonlinear Dynamics and Synchronization pp 33–54Cite as

Multivaluedness Aspects in Self-Organization, Complexity and Computations Investigations by Strong Anticipation

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Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 109))

Abstract

Since the introduction of strong anticipation by D. Dubois, numerous investigations of concrete systems have been proposed. In this chapter, new examples of discrete dynamical systems with anticipation are considered. The mathematical formulation of problems, possible analytical formulas for solutions, and numerical examples of possible solutions are proposed. One of the most interesting properties in such systems is the possible multivaluedness of the solutions. This can be considered from the point of view of dynamical chaos and complex behavior. We present examples of periodic and complex solutions, properties of attractors, and possible applications in self-organization. The main peculiarity is the strong anticipation property. General new possibilities include the possible multivaluedness of the dynamics of automata. Possible interpretations of such behavior of cellular automata are discussed. Further prospects for development of automata theory and hypercomputation are proposed.

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Acknowledgements

The author would like to express his appreciation to D. Krusinsky, Yu. Yatsuk, V. Biliuga, A. Stashenko, and S. Lazarenko for computer realizations of models and to V. Statkevich for assistance in preparing the text of this chapter.

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Authors and Affiliations

  1. Institute for Applied System Analysis at National Tech. University of Ukraine (KPI), Kyiv, Ukraine

    Alexander Makarenko

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  1. Alexander Makarenko
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Correspondence to Alexander Makarenko .

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Editors and Affiliations

  1. Lakeside Park, Alpen-Adria Universität Klagenfurt , Klagenfurt, Austria

    Kyandoghere Kyamakya

  2. Institut für Theoretische Elektrotechnik, Leibniz Universität Hannover, Hannover, Germany

    Wolfgang Mathis

  3. University of Zürich and ETH Zürich, Institute of Neuroinformatics , Zürich, Switzerland

    Ruedi Stoop

  4. Lakeside Park, Alpen-Adria Universität Klagenfurt , Klagenfurt, Austria

    Jean Chamberlain Chedjou

  5. Philipp-Reis-Gebäude, Fernuniversität Hagen , Hagen, Germany

    Zhong Li

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Makarenko, A. (2018). Multivaluedness Aspects in Self-Organization, Complexity and Computations Investigations by Strong Anticipation. In: Kyamakya, K., Mathis, W., Stoop, R., Chedjou, J., Li, Z. (eds) Recent Advances in Nonlinear Dynamics and Synchronization. Studies in Systems, Decision and Control, vol 109. Springer, Cham. https://doi.org/10.1007/978-3-319-58996-1_3

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  • DOI: https://doi.org/10.1007/978-3-319-58996-1_3

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