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Modeling Time in Computing pp 61–79Cite as

Dynamical Systems

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Abstract

In this chapter, we recall, though well-known examples, the main concepts and definitions concerning dynamical systems. We introduce the classic notion of state-space representation of discrete-time and of continuous-time dynamical systems, and we discuss how one can move from the latter to the former. This chapter also briefly presents cellular automata, a family of discrete-time dynamical systems than can be used to model computations. Using the dimensions presented in Chap. 3 as reference, the chapter then describes the main features of the representation of time in dynamical systems.

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Notes

  1. 1.

    The attribute “dynamical” comes from the Greek word for “force” (\(\delta \upsilon \nu \alpha \mu \mathrm{o}\sigma \)), which is the source of system evolution in mechanical phenomena.

  2. 2.

    For simplicity, we assume that the value of constant 1 ∕ (RC) does not impact the precision of the calculation.

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Authors and Affiliations

  1. Department of Computer Science, Zürich, Switzerland

    Carlo A. Furia

  2. Dipartimento di Elettronica e Informazione, Politecnico di Milano, Milan, Italy

    Dino Mandrioli, Angelo Morzenti & Matteo Rossi

Authors
  1. Carlo A. Furia
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  2. Dino Mandrioli
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  3. Angelo Morzenti
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  4. Matteo Rossi
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Furia, C.A., Mandrioli, D., Morzenti, A., Rossi, M. (2012). Dynamical Systems. In: Modeling Time in Computing. Monographs in Theoretical Computer Science. An EATCS Series. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32332-4_4

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  • DOI: https://doi.org/10.1007/978-3-642-32332-4_4

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  • Print ISBN: 978-3-642-32331-7

  • Online ISBN: 978-3-642-32332-4

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