399 research outputs found

    The influence of persuasion in opinion formation and polarization

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    We present a model that explores the influence of persuasion in a population of agents with positive and negative opinion orientations. The opinion of each agent is represented by an integer number kk that expresses its level of agreement on a given issue, from totally against k=Mk=-M to totally in favor k=Mk=M. Same-orientation agents persuade each other with probability pp, becoming more extreme, while opposite-orientation agents become more moderate as they reach a compromise with probability qq. The population initially evolves to (a) a polarized state for r=p/q>1r=p/q>1, where opinions' distribution is peaked at the extreme values k=±Mk=\pm M, or (b) a centralized state for r<1r<1, with most opinions around k=±1k=\pm 1. When r1r \gg 1, polarization lasts for a time that diverges as rMlnNr^M \ln N, where NN is the population's size. Finally, an extremist consensus (k=Mk=M or M-M) is reached in a time that scales as r1r^{-1} for r1r \ll 1

    Competition between surface relaxation and ballistic deposition models in scale free networks

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    In this paper we study the scaling behavior of the fluctuations in the steady state WSW_S with the system size NN for a surface growth process given by the competition between the surface relaxation (SRM) and the Ballistic Deposition (BD) models on degree uncorrelated Scale Free networks (SF), characterized by a degree distribution P(k)kλP(k)\sim k^{-\lambda}, where kk is the degree of a node. It is known that the fluctuations of the SRM model above the critical dimension (dc=2d_c=2) scales logarithmically with NN on euclidean lattices. However, Pastore y Piontti {\it et. al.} [A. L. Pastore y Piontti {\it et. al.}, Phys. Rev. E {\bf 76}, 046117 (2007)] found that the fluctuations of the SRM model in SF networks scale logarithmically with NN for λ<3\lambda <3 and as a constant for λ3\lambda \geq 3. In this letter we found that for a pure ballistic deposition model on SF networks WSW_S scales as a power law with an exponent that depends on λ\lambda. On the other hand when both processes are in competition, we find that there is a continuous crossover between a SRM behavior and a power law behavior due to the BD model that depends on the occurrence probability of each process and the system size. Interestingly, we find that a relaxation process contaminated by any small contribution of ballistic deposition will behave, for increasing system sizes, as a pure ballistic one. Our findings could be relevant when surface relaxation mechanisms are used to synchronize processes that evolve on top of complex networks.Comment: 8 pages, 6 figure

    Fluctuations of a surface relaxation model in interacting scale free networks

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    Isolated complex networks have been studied deeply in the last decades due to the fact that many real systems can be modeled using these types of structures. However, it is well known that the behavior of a system not only depends on itself, but usually also depends on the dynamics of other structures. For this reason, interacting complex networks and the processes developed on them have been the focus of study of many researches in the last years. One of the most studied subjects in this type of structures is the Synchronization problem, which is important in a wide variety of processes in real systems. In this manuscript we study the synchronization of two interacting scale-free networks, in which each node has keke dependency links with different nodes in the other network. We map the synchronization problem with an interface growth, by studying the fluctuations in the steady state of a scalar field defined in both networks. We find that as keke slightly increases from ke=0ke=0, there is a really significant decreasing in the fluctuations of the system. However, this considerable improvement takes place mainly for small values of keke, when the interaction between networks becomes stronger there is only a slight change in the fluctuations. We characterize how the dispersion of the scalar field depends on the internal degree, and we show that a combination between the decreasing of this dispersion and the integer nature of our growth model are the responsible for the behavior of the fluctuations with keke.Comment: 11 pages, 4 figures and 1 tabl

    Interacting social processes on interconnected networks

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    We propose and study a model for the interplay between two different dynamical processes --one for opinion formation and the other for decision making-- on two interconnected networks AA and BB. The opinion dynamics on network AA corresponds to that of the M-model, where the state of each agent can take one of four possible values (S=2,1,1,2S=-2,-1,1,2), describing its level of agreement on a given issue. The likelihood to become an extremist (S=±2S=\pm 2) or a moderate (S=±1S=\pm 1) is controlled by a reinforcement parameter r0r \ge 0. The decision making dynamics on network BB is akin to that of the Abrams-Strogatz model, where agents can be either in favor (S=+1S=+1) or against (S=1S=-1) the issue. The probability that an agent changes its state is proportional to the fraction of neighbors that hold the opposite state raised to a power β\beta. Starting from a polarized case scenario in which all agents of network AA hold positive orientations while all agents of network BB have a negative orientation, we explore the conditions under which one of the dynamics prevails over the other, imposing its initial orientation. We find that, for a given value of β\beta, the two-network system reaches a consensus in the positive state (initial state of network AA) when the reinforcement overcomes a crossover value r(β)r^*(\beta), while a negative consensus happens for r<r(β)r<r^*(\beta). In the rβr-\beta phase space, the system displays a transition at a critical threshold βc\beta_c, from a coexistence of both orientations for β<βc\beta<\beta_c to a dominance of one orientation for β>βc\beta>\beta_c. We develop an analytical mean-field approach that gives an insight into these regimes and shows that both dynamics are equivalent along the crossover line (r,β)(r^*,\beta^*).Comment: 25 pages, 6 figure

    Synchronization in interacting Scale Free Networks

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    We study the fluctuations of the interface, in the steady state, of the Surface Relaxation Model (SRM) in two scale free interacting networks where a fraction qq of nodes in both networks interact one to one through external connections. We find that as qq increases the fluctuations on both networks decrease and thus the synchronization reaches an improvement of nearly 40%40\% when q=1q=1. The decrease of the fluctuations on both networks is due mainly to the diffusion through external connections which allows to reducing the load in nodes by sending their excess mostly to low-degree nodes, which we report have the lowest heights. This effect enhances the matching of the heights of low-and high-degree nodes as qq increases reducing the fluctuations. This effect is almost independent of the degree distribution of the networks which means that the interconnection governs the behavior of the process over its topology.Comment: 13 pages, 7 figures. Added a relevant reference.Typos fixe

    Recovery of Interdependent Networks

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    Recent network research has focused on the cascading failures in a system of interdependent networks and the necessary preconditions for system collapse. An important question that has not been addressed is how to repair a failing system before it suffers total breakdown. Here we introduce a recovery strategy of nodes and develop an analytic and numerical framework for studying the concurrent failure and recovery of a system of interdependent networks based on an efficient and practically reasonable strategy. Our strategy consists of repairing a fraction of failed nodes, with probability of recovery γ\gamma, that are neighbors of the largest connected component of each constituent network. We find that, for a given initial failure of a fraction 1p1-p of nodes, there is a critical probability of recovery above which the cascade is halted and the system fully restores to its initial state and below which the system abruptly collapses. As a consequence we find in the plane γp\gamma-p of the phase diagram three distinct phases. A phase in which the system never collapses without being restored, another phase in which the recovery strategy avoids the breakdown, and a phase in which even the repairing process cannot avoid the system collapse

    Evolution equation for a model of surface relaxation in complex networks

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    In this paper we derive analytically the evolution equation of the interface for a model of surface growth with relaxation to the minimum (SRM) in complex networks. We were inspired by the disagreement between the scaling results of the steady state of the fluctuations between the discrete SRM model and the Edward-Wilkinson process found in scale-free networks with degree distribution P(k)kλ P(k) \sim k^{-\lambda} for λ<3\lambda <3 [Pastore y Piontti {\it et al.}, Phys. Rev. E {\bf 76}, 046117 (2007)]. Even though for Euclidean lattices the evolution equation is linear, we find that in complex heterogeneous networks non-linear terms appear due to the heterogeneity and the lack of symmetry of the network; they produce a logarithmic divergency of the saturation roughness with the system size as found by Pastore y Piontti {\it et al.} for λ<3\lambda <3.Comment: 9 pages, 2 figure
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