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Topological Perturbations and Their Effect on the Dynamics of Totalistic Cellular Automata

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Cellular Automata (ACRI 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7495))

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Abstract

Although several studies addressed the dynamical properties of cellular automata (CAs) in general and the sensitivity to the initial condition from which they are evolved in particular, only minor attention has been paid to the interference between a CA’s dynamics and its underlying topology, by which we refer to the whole of a CA’s spatial entities and their interconnection. Nevertheless, some preliminary studies highlighted the importance of this issue. Henceforth, in contrast to the sensitivity to the initial conditions, which is frequently quantified by means of Lyapunov exponents, to this day no methodology is available for grasping this so-called topological sensitivity. Inspired by the concept of classical Lyapunov exponents, we elaborate on the machinery that is required to grasp the topological sensitivity of CAs, which consists of topological Lyapunov exponents and Jacobians. By relying on these concepts, the topological sensitivity of a family of 2-state irregular totalistic CAs is characterized.

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Author information

Authors and Affiliations

  1. KERMIT, Department of Mathematical Modelling, Statistics and Bioinformatics, Ghent University, Coupure links 653, Gent, Belgium

    Jan M. Baetens & Bernard De Baets

Authors
  1. Jan M. Baetens
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  2. Bernard De Baets
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Editor information

Editors and Affiliations

  1. Department of Electrical and Computer Engineering, Laboratory of Electronics, Democritus University of Thrace, GR 67100, Xanthi, Greece

    Georgios Ch. Sirakoulis

  2. CSAI - Complex Systems and Artificial Intelligence Research Center, University of Milano-Bicocca, 20134, Milano, Italy

    Stefania Bandini

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© 2012 Springer-Verlag Berlin Heidelberg

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Baetens, J.M., De Baets, B. (2012). Topological Perturbations and Their Effect on the Dynamics of Totalistic Cellular Automata. In: Sirakoulis, G.C., Bandini, S. (eds) Cellular Automata. ACRI 2012. Lecture Notes in Computer Science, vol 7495. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33350-7_1

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  • DOI: https://doi.org/10.1007/978-3-642-33350-7_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-33349-1

  • Online ISBN: 978-3-642-33350-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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