Analytical and numerical study of the non-linear noisy voter model on complex networks

Peralta, Antonio F.; Carro, Adrián; Miguel, M. San; Toral, Raúl

doi:10.1063/1.5030112

Cited by 77 publications

(113 citation statements)

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“…We present in this appendix a simpler method, based on a master equation approach, to compute the statistical properties of the link magnetization, including fluctuations and finite-size effects [53]. This approach is very similar to the all-to-all approximation, and it can be derived following the same steps.…”

Section: Appendix D Master Equation For the Link Magnetizationmentioning

confidence: 99%

“…Many works based on these approaches have further neglected dynamical correlations, fluctuations and finite-size effects, which corresponds to a mean-field type of analysis. While there have been attempts to relax these restrictions and deal with finite-size effects, these efforts have been usually based on an adiabatic elimination of variables [37,43,48,49,[51][52][53], whose range of validity is limited.In this paper we consider this intermediate level of description focusing on the PA that chooses as a reduced set of relevant variables the number of nodes with a given degree in a given state and the number of links connecting nodes in different states. We develop a full stochastic treatment of the PA scheme in which we avoid mean-field analysis or adiabatic elimination of variables.…”

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confidence: 99%

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Stochastic pair approximation treatment of the noisy voter model

et al. 2018

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We present a full stochastic description of the pair approximation scheme to study binary-state dynamics on heterogeneous networks. Within this general approach, we obtain a set of equations for the dynamical correlations, fluctuations and finite-size effects, as well as for the temporal evolution of all relevant variables. We test this scheme for a prototypical model of opinion dynamics known as the noisy voter model that has a finite-size critical point. Using a closure approach based on a system size expansion around a stochastic dynamical attractor we obtain very accurate results, as compared with numerical simulations, for stationary and time-dependent quantities whether below, within or above the critical region. We also show that finite-size effects in complex networks cannot be captured, as often suggested, by merely replacing the actual system size N by an effective network dependent size N eff . IntroductionFrom classical problems in statistical physics [1, 2] to questions in biology and ecology [3][4][5], and over to the spreading of opinions and diseases in social systems [6-10], stochastic binary-state models have been widely used to study the emergence of collective phenomena in systems of stochastically interacting components. In general, these components are modeled as binary-state variables -spin up or down-sitting at the nodes of a network whose links represent the possible interactions among them. While initial research focused on the limiting cases of a well-mixed population, where each of the components is allowed to interact with any other, and regular lattice structures, later works turned to more complex and heterogeneous topologies [11][12][13][14]. A most important insight derived from these more recent works is that the macroscopic dynamics of the system can be greatly affected by the particular topology of the underlying network. In the case of systems with critical behavior, different network characteristics have been shown to have a significant impact on the critical values of the model parameters [15][16][17], such as the critical temperature of the Ising model [18][19][20] and the epidemic threshold in models of infectious disease transmission [21][22][23][24][25]. Thus, the identification of the particular network characteristics that have an impact on the dynamics of these models, as well as the quantification of their effect, are of paramount importance.The first theoretical treatments introduced for the study of stochastic, binary-state dynamics on networks relied on a global-state approach [2, 26], i.e. they focused on a single variable-for example, the number of nodes in one of the two possible states-assumed to represent the whole state of the system. In order to write a master equation for this global-state variable, some approximation is required to move from the individual particle transition rates defining the model to some effective transition rates depending only on the chosen global variable. Within this global-state approach, the effective-field approximation assumes...

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Section: Appendix D Master Equation For the Link Magnetizationmentioning

confidence: 99%

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confidence: 99%

Stochastic pair approximation treatment of the noisy voter model

et al. 2018

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“…Second, the nonlinearity parameterq measures the effect of local group interactions. Nonlinearity is mathematically implemented as a k q i i ( ) [36,[38][39][40][41]. When q=1, our model becomes the ordinary coevolving linear voter model [34].…”

Section: Modelmentioning

confidence: 99%

“…Specifically, a coevolving nonlinear voter model (CNVM) has been studied in order to incorporate collective interactions and coevolution dynamics at the same time [36]. The nonlinearity in the CNVM takes into account that the state of an agent is affected by the state of all of their neighbors as a whole, and not by a pairwise interaction [38][39][40][41]. The nonlinear interaction gives rise to diverse phases, with different mechanisms for fragmentation transitions.…”

Section: Introductionmentioning

confidence: 99%

Multilayer coevolution dynamics of the nonlinear voter model

Min

Miguel

2019

New J. Phys.

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We study a coevolving nonlinear voter model (CNVM) on a two-layer network. Coevolution stands for coupled dynamics of the state of the nodes and of the topology of the network in each layer. The plasticity parameter p measures the relative time scale of the evolution of the states of the nodes and the evolution of the network by link rewiring. Nonlinearity of the interactions is taken into account through a parameterq that describes the nonlinear effect of local majorities being q=1 the marginal situation of the ordinary voter model. Finally the connection between the two layers is measured by a degree of multiplexing ℓ. In terms of these three parameters,p, q and ℓ we find a rich phase diagram with different phases and transitions. When the two layers have the same plasticity p, the fragmentation transition observed in a single layer is shifted to larger values of p plasticity, so that multiplexing avoids fragmentation. Different plasticities for the two layers lead to new phases that do not exist in a CNVM in a single layer, namely an asymmetric fragmented phase for q>1 and an active shattered phase for q<1. Coupling layers with different types of nonlinearity, q 1 <1 and q 2 >1, we can find two different transitions by increasing the plasticity parameter, a first absorbing transition with no fragmentation and a subsequent fragmentation transition.

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“…In the next contribution, the article by Peralta et al (2018) considers a well-established model of social behavior based on a mechanism of imitation. The main idea is to understand under which rules a society, or a group of people, can reach consensus on a given topic, considering (i) the influence of the network of interactions amongst the people, (ii) the eventual desire to depart from the group main behavior, and (iii) the reluctance to change opinion despite the majority consensus.…”

Section: Introductionmentioning

confidence: 99%