139 research outputs found
Competition between surface relaxation and ballistic deposition models in scale free networks
In this paper we study the scaling behavior of the fluctuations in the steady
state with the system size 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 , where is the degree of a node.
It is known that the fluctuations of the SRM model above the critical dimension
() scales logarithmically with 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 for and as a constant
for . In this letter we found that for a pure ballistic
deposition model on SF networks scales as a power law with an exponent
that depends on . 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
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 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 slightly increases from , there is a really
significant decreasing in the fluctuations of the system. However, this
considerable improvement takes place mainly for small values of , 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 .Comment: 11 pages, 4 figures and 1 tabl
Interacting social processes on interconnected networks
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 A and B. The opinion dynamics on network A corresponds to that of the M-model, where the state of each agent can take one of four possible values (S = -2,-1, 1, 2), describing its level of agreement on a given issue. The likelihood to become an extremist (S = ±2) or a moderate (S = ±1) is controlled by a reinforcement parameter r ≥ 0. The decision making dynamics on network B is akin to that of the Abrams-Strogatz model, where agents can be either in favor (S = +1) or against (S = -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. Starting from a polarized case scenario in which all agents of network A hold positive orientations while all agents of network B 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, the two-network system reaches a consensus in the positive state (initial state of network A) when the reinforcement overcomes a crossover value r∗(β), while a negative consensus happens for r ∗(β). In the r - β phase space, the system displays a transition at a critical threshold βc, from a coexistence of both orientations for β c to a dominance of one orientation for β > βc. 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∗).Facultad de Ciencias ExactasInstituto de FÃsica de LÃquidos y Sistemas Biológico
Critical behavior of cascading failures in overloaded networks
In recent years, research on spatial networks has become of widespread
interest, with the focus on analyzing critical phenomena that can dramatically
affect real systems via cascading failures and abrupt collapses. Here, we study
the breakdown of a spatial network having a characteristic link-length due to
overloads and the cascading failures that are triggered by failures of a
fraction of links. While such breakdowns have been studied extensively, the
critical exponents and the universality class of this phase transition have not
been found. Here, we show indications that this transition has features and
critical exponents which are the same as those of interdependent network
systems, suggesting that both systems are in the same universality class. We
find different abrupt transitions at the steady state, for different spatial
embedding strength. For the weakly embedded systems (i.e., link-lengths of the
order of the system size) we observe a mixed-order transition where the order
parameter collapses with time in a long plateau shape. On the other hand, in
strongly embedded systems (relatively short links), we find a pure first order
transition which involves nucleation and growth of damage. System behavior in
both limits is analogous to that observed in interdependent networks.Comment: 7 pages, 6 figure
Interacting social processes on interconnected networks
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 A and B. The opinion dynamics on network A corresponds to that of the M-model, where the state of each agent can take one of four possible values (S = -2,-1, 1, 2), describing its level of agreement on a given issue. The likelihood to become an extremist (S = ±2) or a moderate (S = ±1) is controlled by a reinforcement parameter r ≥ 0. The decision making dynamics on network B is akin to that of the Abrams-Strogatz model, where agents can be either in favor (S = +1) or against (S = -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. Starting from a polarized case scenario in which all agents of network A hold positive orientations while all agents of network B 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, the two-network system reaches a consensus in the positive state (initial state of network A) when the reinforcement overcomes a crossover value r∗(β), while a negative consensus happens for r ∗(β). In the r - β phase space, the system displays a transition at a critical threshold βc, from a coexistence of both orientations for β c to a dominance of one orientation for β > βc. 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∗).Facultad de Ciencias ExactasInstituto de FÃsica de LÃquidos y Sistemas Biológico
Cascading Failures in Complex Networks
Cascading failure is a potentially devastating process that spreads on
real-world complex networks and can impact the integrity of wide-ranging
infrastructures, natural systems, and societal cohesiveness. One of the
essential features that create complex network vulnerability to failure
propagation is the dependency among their components, exposing entire systems
to significant risks from destabilizing hazards such as human attacks, natural
disasters or internal breakdowns. Developing realistic models for cascading
failures as well as strategies to halt and mitigate the failure propagation can
point to new approaches to restoring and strengthening real-world networks. In
this review, we summarize recent progress on models developed based on physics
and complex network science to understand the mechanisms, dynamics and overall
impact of cascading failures. We present models for cascading failures in
single networks and interdependent networks and explain how different dynamic
propagation mechanisms can lead to an abrupt collapse and a rich dynamic
behavior. Finally, we close the review with novel emerging strategies for
containing cascades of failures and discuss open questions that remain to be
addressed.Comment: This review has been accepted for publication in the Journal of
Complex Networks Published by Oxford University Pres
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