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Author Montalva-Medel, M.; Rica, S.; Urbina, F.
Title Phase space classification of an Ising cellular automaton: The Q2R model Type
Year 2020 Publication Chaos Solitons & Fractals Abbreviated Journal Chaos Solitons Fractals
Volume 133 Issue Pages 14 pp
Keywords
Abstract An exact classification of the different dynamical behaviors that exhibits the phase space of a reversible and conservative cellular automaton, the so-called Q2R model, is shown in this paper. Q2R is a cellular automaton which is a dynamical variation of the Ising model in statistical physics and whose space of configurations grows exponentially with the system size. As a consequence of the intrinsic reversibility of the model, the phase space is composed only by configurations that belong to a fixed point or a cycle. In this work, we classify them in four types accordingly to well differentiated topological characteristics. Three of them -which we call of type S-I, S-II, and S-III- share a symmetry property, while the fourth, which we call of type AS does not. Specifically, we prove that any configuration of Q2R belongs to one of the four previous types of cycles. Moreover, at a combinatorial level, we can determine the number of cycles for some small periods which are almost always present in the Q2R. Finally, we provide a general overview of the resulting decomposition of the arbitrary size Q2R phase space and, in addition, we realize an exhaustive study of a small Ising system (4 x 4) which is thoroughly analyzed under this new framework, and where simple mathematical tools are introduced in order to have a more direct understanding of the Q2R dynamics and to rediscover known properties like the energy conservation. (C) 2020 Elsevier Ltd. All rights reserved.
Address [Montalva-Medel, Marco; Rica, Sergio] Univ Adolfo Ibanez, Fac Ingn & Ciencias, Avda Diagonal Torres 2640, Santiago, Chile
Corporate Author Thesis
Publisher Pergamon-Elsevier Science Ltd Place of Publication Editor
Language English Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 0960-0779 ISBN Medium
Area Expedition Conference
Notes WOS:000520892300040 Approved
Call Number UAI @ eduardo.moreno @ Serial 1130
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Author Ruivo, E.L.P.; Montalva-Medel, M.; de Oliveira, P.P.B.; Perrot, K.
Title Characterisation of the elementary cellular automata in terms of their maximum sensitivity to all possible asynchronous updates Type
Year 2018 Publication Chaos Solitons & Fractals Abbreviated Journal Chaos Solitons Fractals
Volume 113 Issue Pages 209-220
Keywords Cellular automaton; Asynchronous update; Update digraph; Discrete dynamics; One-step maximum sensitivity
Abstract Cellular automata are fully-discrete dynamical systems with global behaviour depending upon their locally specified state transitions. They have been extensively studied as models of complex systems as well as objects of mathematical and computational interest. Classically, the local rule of a cellular automaton is iterated synchronously over the entire configuration. However, the question of how asynchronous updates change the behaviour of a cellular automaton has become a major issue in recent years. Here, we analyse the elementary cellular automata rule space in terms of how many different one-step trajectories a rule would entail when taking into account all possible deterministic ways of updating the rule, for one time step, over all possible initial configurations. More precisely, we provide a characterisation of the elementary cellular automata, by means of their one-step maximum sensitivity to all possible update schedules, that is, the property that any change in the update schedule causes the rule's one-step trajectories also to change after one iteration. Although the one-step maximum sensitivity does not imply that the remainder of the time-evolutions will be distinct, it is a necessary condition for that. (C) 2018 Elsevier Ltd. All rights reserved.
Address [Ruivo, Eurico L. P.; de Oliveira, Pedro P. B.] Univ Presbiteriana Mackenzie, Fac Comp & Informat, Sao Paulo, SP, Brazil, Email: eurico.ruivo@mackenzie.br
Corporate Author Thesis
Publisher Pergamon-Elsevier Science Ltd Place of Publication Editor
Language English Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 0960-0779 ISBN Medium
Area Expedition Conference
Notes WOS:000442101600024 Approved
Call Number UAI @ eduardo.moreno @ Serial 910
Permanent link to this record