Real Linear Automata with a Continuum of Periodic Solutions for Every Period

XU, Xu (2019). Real Linear Automata with a Continuum of Periodic Solutions for Every Period. International Journal of Bifurcation and Chaos, 29 (6).

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Official URL: https://www.worldscientific.com/doi/abs/10.1142/S0...
Link to published version:: https://doi.org/10.1142/S0218127419300167

Abstract

Interesting dynamical features such as periodic solutions of binary cellular automata are rare and therefore difficult to find, in general. In this paper, we illustrate an effective method in identifying fixed and periodic points of traditional one- and two-dimensional p p-valued cellular automaton systems, using cycle graphs. We also show that when the binary or p p-valued cellular states are extended to real-values and when defined as doubly-infinite vectors, there exists a continuum of periodic solutions for every period, even when the governing local rules are simply linear. In addition, we demonstrate the important effect that boundary conditions have on systems’ dynamical structures.

Item Type: Article
Uncontrolled Keywords: 0102 Applied Mathematics; 0103 Numerical And Computational Mathematics; 0913 Mechanical Engineering; Fluids & Plasmas
Identification Number: https://doi.org/10.1142/S0218127419300167
SWORD Depositor: Symplectic Elements
Depositing User: Symplectic Elements
Date Deposited: 28 Jan 2019 09:31
Last Modified: 08 Jul 2019 10:55
URI: http://shura.shu.ac.uk/id/eprint/23867

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