Phase Transitions of Cellular Automata

Bagnoli, Franco; Rechtman, Raúl

doi:10.1007/978-3-319-65558-1_15

Cited by 4 publications

(4 citation statements)

References 27 publications

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“…Mean-field models, as well as the maps, are "well stirred," while the PCA dynamics is local. One way to recover the bifurcations is to add some reshuffling (long-range mixing) among the interacting particles or to rewire a fraction of the cells to explore the small-world effect (see [53,61,62] for examples, discussion, and references).…”

Section: Discussionmentioning

confidence: 99%

“…Most PCA models in the literature are one and twoparameter models, since they are already rich and flexible enough to model a great many phenomena, in one or more dimensions, and display a variety of nontrivial behavior, from disordered and chaotic phases to phase transitions of several different kinds [2][3][4][5][6][51][52][53][54]. It is thus not entirely without interest to identify single-parameter PCA that in the single-cell mean-field approximation yield models for the logistic growth of populations, with or without weak Allee effects.…”

Section: Single-parameter Pcamentioning

confidence: 99%

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Approximate probabilistic cellular automata for the dynamics of single-species populations under discrete logisticlike growth with and without weak Allee effects

Mendonça

Gevorgyan

2017

Phys. Rev. E

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We investigate one-dimensional elementary probabilistic cellular automata (PCA) whose dynamics in first-order mean-field approximation yields discrete logisticlike growth models for a single-species unstructured population with nonoverlapping generations. Beginning with a general six-parameter model, we find constraints on the transition probabilities of the PCA that guarantee that the ensuing approximations make sense in terms of population dynamics and classify the valid combinations thereof. Several possible models display a negative cubic term that can be interpreted as a weak Allee factor. We also investigate the conditions under which a one-parameter PCA derived from the more general six-parameter model can generate valid population growth dynamics. Numerical simulations illustrate the behavior of some of the PCA found.

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Section: Discussionmentioning

confidence: 99%

Section: Single-parameter Pcamentioning

confidence: 99%

Approximate probabilistic cellular automata for the dynamics of single-species populations under discrete logisticlike growth with and without weak Allee effects

Mendonça

Gevorgyan

2017

Phys. Rev. E

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“…We refer to the progress of the percolation process with the term "infection" and to the region of phase space where in the long-time limit there is a finite probability of survival for the percolation process as the "active" region (ρ > 0), see Figure 1. One can show that the standard site (directed) percolation corresponds to the line q = p and that the bond (directed) percolation corresponds to the curve q = p(1 − 2p), but other interesting behaviors occurs in the p − q phase space, in particular near the corner p = 1, q = 0 (chaotic phase, Figure 1) that corresponds to a disruptive interference for which percolation can happen more easily if there is just one "infected" neighbors than if there are two [23,24].…”

Section: Percolation and Directed Percolationmentioning

confidence: 99%

From Color-Avoiding to Color-Favored Percolation in Diluted Lattices

Giusfredi

Bagnoli

2020

Future Internet

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We study the problem of color-avoiding and color-favored percolation in a network, i.e., the problem of finding a path that avoids a certain number of colors, associated with vulnerabilities of nodes or links, or is attracted by them. We investigate here regular (mainly directed) lattices with a fractions of links removed (hence the term “diluted”). We show that this problem can be formulated as a self-organized critical problem, in which the asymptotic phase space can be obtained in one simulation. The method is particularly effective for certain “convex” formulations, but can be extended to arbitrary problems using multi-bit coding. We obtain the phase diagram for some problem related to color-avoiding percolation on directed models. We also show that the interference among colors induces a paradoxical effect in which color-favored percolation is permitted where standard percolation for a single color is impossible.

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“…By varying T, one gets the view of the bifurcation of Figure 3 as a variation of the minima of F, as shown in Figure 4. More details about phase transition in percolation, Ising and cellular automata models can be found in [61].…”

Section: The Time Average Of An Observable Ismentioning

confidence: 99%

Percolation and Internet Science

et al. 2019

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Percolation, in its most general interpretation, refers to the “flow” of something (a physical agent, data or information) in a network, possibly accompanied by some nonlinear dynamical processes on the network nodes (sometimes denoted reaction–diffusion systems, voter or opinion formation models, etc.). Originated in the domain of theoretical and matter physics, it has many applications in epidemiology, sociology and, of course, computer and Internet sciences. In this review, we illustrate some aspects of percolation theory and its generalization, cellular automata and briefly discuss their relationship with equilibrium systems (Ising and Potts models). We present a model of opinion spreading, the role of the topology of the network to induce coherent oscillations and the influence (and advantages) of risk perception for stopping epidemics. The models and computational tools that are briefly presented here have an application to the filtering of tainted information in automatic trading. Finally, we introduce the open problem of controlling percolation and other processes on distributed systems.

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Phase Transitions of Cellular Automata

Cited by 4 publications

References 27 publications

Approximate probabilistic cellular automata for the dynamics of single-species populations under discrete logisticlike growth with and without weak Allee effects

Approximate probabilistic cellular automata for the dynamics of single-species populations under discrete logisticlike growth with and without weak Allee effects

From Color-Avoiding to Color-Favored Percolation in Diluted Lattices

Percolation and Internet Science

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