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Finite Size Stability Analysis for Stochastic Cellular Automata

  • Conference paper
Cellular Automata (ACRI 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5191))

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Abstract

Real simulations are performed on a finite size of lattice. It is therefore very difficult to predict a phase diagram on an infinitely large lattice. Here, we present a Finite Size Stability Analysis (FSSA) to know whether the phase is sustainable or not. Although this analysis is a hypothesis, it enables us to determine the boundary of phase diagram. We apply FSSA to multi-state system. For example we study ten-species system in ecology. From computer simulations on various sizes of lattices, we obtain the waiting time τ to extinction. The system is found to have two phases: the coexistence of all species is either unstable or marginally (neutrally) stable. In the latter case, τ diverges on a power law with the increase of lattice size.

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Authors and Affiliations

  1. Ibaraki Prefectural University of Health Sciences, Ami, 300-0394, Japan

    Yukio Sakisaka & Yukio Iwamura

  2. University of Hyogo, Himeji, 670-0092, Japan

    Nariyuki Nakagiri

  3. Shizuoka University, Hamamatsu, 432-8561, Japan

    Jin Yoshimura & Kei-ichi Tainaka

Authors
  1. Yukio Sakisaka
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  2. Yukio Iwamura
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  3. Nariyuki Nakagiri
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  4. Jin Yoshimura
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  5. Kei-ichi Tainaka
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Editor information

Hiroshi Umeo Shin Morishita Katsuhiro Nishinari Toshihiko Komatsuzaki Stefania Bandini

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© 2008 Springer-Verlag Berlin Heidelberg

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Sakisaka, Y., Iwamura, Y., Nakagiri, N., Yoshimura, J., Tainaka, Ki. (2008). Finite Size Stability Analysis for Stochastic Cellular Automata. In: Umeo, H., Morishita, S., Nishinari, K., Komatsuzaki, T., Bandini, S. (eds) Cellular Automata. ACRI 2008. Lecture Notes in Computer Science, vol 5191. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79992-4_29

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  • DOI: https://doi.org/10.1007/978-3-540-79992-4_29

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-79991-7

  • Online ISBN: 978-3-540-79992-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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