On the Dynamical Behavior of Cellular Automata

Xu, Xu; Song, Yi; Banks, Stephen P.

doi:10.1142/s021812740902355x

Cited by 10 publications

(11 citation statements)

References 13 publications

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“…In this paper, a previously discovered graph theory based technique [Xu et al, 2009] for finding period solutions of one-dimensional binary automata has been extended to two-dimensional and p-valued CA.…”

Section: Discussionmentioning

confidence: 99%

“…Hence F 2 is equivalent to a system with neighbourhood length 4q + 1 [Xu et al, 2009]. It follows that, in order to study periodic solutions of period m, we can consider the fixed points of an equivalent system F m with neighbourhood length 2mq + 1.…”

Section: Periodic Solutions Of Discrete Cellular Systemsmentioning

confidence: 99%

“…Furthermore, CA have also been studied as spatially and temporally discrete nonlinear dynamical systems. In our previous work [Xu et al, 2009], we classified one-dimensional (1D) binary CA based on Smale's basic sets and nonwandering points as well as introducing mathematical and numerical techniques for identifying periodic points and basic sets. These share a common perspective as Mainzer and Chua's work [Mainzer & Chua, 2011] and many of the results agree.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

2019

Int. J. Bifurcation Chaos

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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 [Formula: see text]-valued cellular automaton systems, using cycle graphs. We also show that when the binary or [Formula: see text]-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.

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Section: Discussionmentioning

confidence: 99%

Section: Periodic Solutions Of Discrete Cellular Systemsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

2019

Int. J. Bifurcation Chaos

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“…As a result, analyzing the new growth patch's spatial dependence is necessary when studying urban growth and its effect in the CA model. Similar to the buffering procedure used by Xu et al [38], Schneider [39] and Shi et al [40], the newly-developed urban patch polygons were overlaid with a hundred buffer zones at 0.3 km from district centers ( Figure 2a) and fifty buffer zones at 0.06 km from main roads (Figure 2b). These buffer zones were used to extract and calculate the area of the newly developed urban patch in each buffer ring.…”

Section: Indicators For Measuring Urban Growthmentioning

confidence: 99%

Analysis of the Effectiveness of Urban Land-Use-Change Models Based on the Measurement of Spatio-Temporal, Dynamic Urban Growth: A Cellular Automata Case Study

Liu

Long

et al. 2017

Sustainability

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Developing countries have been undergoing dramatic urban growth over the past three decades. It is essential to understand and simulate the urban growth process for smart urban planning and sustainable development purposes. Cellular automata (CA) modeling is an efficient approach to simulating urban land use/cover change; however, the traditional CA method has limitations in simulating the various urban growth patterns and processes. This study aims to analyze the influences of different urban growth characteristics on the effectiveness of CA modeling by conducting a case study over the area in the Pearl River Delta of Southern China. We used the growth rate, landscape expansion index, and spatial dependency to quantify the urban growth characteristics. The effectiveness of CA modeling was measured through a comparison of the simulation results with the reference data. The simulation results and validation analyses reveal that the traditional CA is not applicable for the following three situations: (1) the urban growth pattern characterized by less growth area or a higher ratio of outlying expansion; (2) the urban region that includes several subregions with disparate growth characteristics; and (3) the existence of temporal differences in growth characteristics over a long period.

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“…To measure the chaotic behavior in dynamical systems were announced several studies that involved both geometrical [30] and statistical [31] approaches. The statistical approach, seeks to characterize dynamical systems through the Lyapunov exponent, which has been proven to be the most useful to measure chaos [32], [33], [34], [35].…”

Section: B Chaotic Cellular Automatamentioning

confidence: 99%

Chaotic encryption method based on life-like cellular automata

Machicao

Marco

Bruno

2012

Expert Systems with Applications

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Abstract-We propose a chaotic encryption method based on Cellular Automata(CA), specifically on the family called the "Life-Like" type. Thus, the encryption process lying on the pseudo-random numbers generated (PRNG) by each CA's evolution, which transforms the password as the initial conditions to encrypt messages. Moreover, is explored the dynamical behavior of CA to reach a "good" quality as PRNG based on measures to quantify "how chaotic a dynamical system is", through the combination of the entropy, Lyapunov exponent, and Hamming distance. Finally, we present the detailed security analysis based on experimental tests: DIEHARD and ENT suites, as well as Fouriers Power Spectrum, used as a security criteria.

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On the Dynamical Behavior of Cellular Automata

Cited by 10 publications

References 13 publications

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

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

Analysis of the Effectiveness of Urban Land-Use-Change Models Based on the Measurement of Spatio-Temporal, Dynamic Urban Growth: A Cellular Automata Case Study

Chaotic encryption method based on life-like cellular automata

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