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Symbolic dynamics of glider guns for some one-dimensional cellular automata

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Abstract

By exploiting the characteristic function, Lameray diagram, and forward time-\(\tau \) map of one-dimensional cellular automata (1D CAs), an empirical observation of long-term time-asymptotic behaviors of glider guns is achieved. Based on this qualitative property, the mathematical definition of glider gun for 1D CAs is proposed from the viewpoint of symbolic dynamics. Moreover, its underlying asymptotic dynamics is characterized in subtle detail, demonstrating that the dynamic evolution of glider gun converges to the limit cycle. This conclusion holds for all general 1D CAs, which is an extended discovery in both CAs and nonlinear dynamics. Meanwhile, chaotic dynamics of gliders is excavated to illustrate rich and complicated dynamical behaviors of guns. For the examples, glider guns of rules 54 and 110 are offered to present the constructive procedures described in this paper.

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Acknowledgments

This research was jointly supported by NSFC (Grants No. 11171084 and 60872093) and Foundation of Zhejiang Education Department (Grant No. Y201534584).

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Authors and Affiliations

  1. College of Pharmaceutical Sciences, Zhejiang Chinese Medical University, Hangzhou, Zhejiang, China

    Weifeng Jin

  2. School of Science, Shanghai University, Shanghai, China

    Weifeng Jin & Fangyue Chen

  3. School of Science, Hangzhou Dianzi University, Hangzhou, Zhejiang, China

    Fangyue Chen

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  1. Weifeng Jin
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  2. Fangyue Chen
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Correspondence to Weifeng Jin.

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Jin, W., Chen, F. Symbolic dynamics of glider guns for some one-dimensional cellular automata. Nonlinear Dyn 86, 941–952 (2016). https://doi.org/10.1007/s11071-016-2935-6

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  • DOI: https://doi.org/10.1007/s11071-016-2935-6

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