Phase transitions of extended-range probabilistic cellular automata with two absorbing states

Bagnoli, Franco; Franci, Fabio; Rechtman, Raúl

doi:10.1103/physreve.71.046108

Cited by 7 publications

(10 citation statements)

References 26 publications

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“…In this case, we have the stability of the two absorbing states for J > 0 (conformist society or ordered phase), while for J < 0 (anti-ferro or contrarian) the absorbing states are unstable and a new, disordered active phase is observed. The model has been studied in the one-dimensional case with larger neighborhood [10]. In this case one observes again the transition from an ordered to an active, microscopically disordered phase, but with no coherent oscillations.…”

Section: The Modelmentioning

confidence: 97%

Topological bifurcations in a model society of reasonable contrarians

Bagnoli

Rechtman

2013

Phys. Rev. E

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People are often divided into conformists and contrarians, the former tending to align to the majority opinion in their neighborhood and the latter tending to disagree with that majority. In practice, however, the contrarian tendency is rarely followed when there is an overwhelming majority with a given opinion, which denotes a social norm. Such reasonable contrarian behavior is often considered a mark of independent thought and can be a useful strategy in financial markets. We present the opinion dynamics of a society of reasonable contrarian agents. The model is a cellular automaton of Ising type, with antiferromagnetic pair interactions modeling contrarianism and plaquette terms modeling social norms. We introduce the entropy of the collective variable as a way of comparing deterministic (mean-field) and probabilistic (simulations) bifurcation diagrams. In the mean-field approximation the model exhibits bifurcations and a chaotic phase, interpreted as coherent oscillations of the whole society. However, in a one-dimensional spatial arrangement one observes incoherent oscillations and a constant average. In simulations on Watts-Strogatz networks with a small-world effect the mean-field behavior is recovered, with a bifurcation diagram that resembles the mean-field one but where the rewiring probability is used as the control parameter. Similar bifurcation diagrams are found for scale-free networks, and we are able to compute an effective connectivity for such networks.

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Section: The Modelmentioning

confidence: 97%

Topological bifurcations in a model society of reasonable contrarians

Bagnoli

Rechtman

2013

Phys. Rev. E

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“…Wolfram exhaustively catalogued and classified behaviour of simple deterministic automata [17,18]. Phase diagrams and critical exponents have been evaluated for automata with absorbing states [19][20][21][22][23]. Certain probabilistic automata have been shown to fall into the same universality class as directed percolation [24,25].…”

Section: Introductionmentioning

confidence: 99%

When are cellular automata random?

Coe

Ahnert²,

Fink

2008

Europhys. Lett.

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“…[28] and Section II). However, one should consider that chaotic oscillations on networks easily desynchronize, and the resulting "microscopic chaos" is quite different from the synchronous oscillations predicted by mean-field analysis [29], that may nevertheless be observed in lattice models the presence of long-range coupling [30].…”

Section: Introductionmentioning

confidence: 99%

Risk perception in epidemic modeling

2007

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We investigate the effects of risk perception in a simple model of epidemic spreading. We assume that the perception of the risk of being infected depends on the fraction of neighbors that are ill. The effect of this factor is to decrease the infectivity, that therefore becomes a dynamical component of the model. We study the problem in the mean-field approximation and by numerical simulations for regular, random and scale-free networks. We show that for homogeneous and random networks, there is always a value of perception that stops the epidemics. In the "worst-case" scenario of a scale-free network with diverging input connectivity, a linear perception cannot stop the epidemics; however we show that a non-linear increase of the perception risk may lead to the extinction of the disease. This transition is discontinuous, and is not predicted by the mean-field analysis.

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Phase transitions of extended-range probabilistic cellular automata with two absorbing states

Cited by 7 publications

References 26 publications

Topological bifurcations in a model society of reasonable contrarians

Topological bifurcations in a model society of reasonable contrarians

When are cellular automata random?

Risk perception in epidemic modeling

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