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 ($S=\pm 2$) or a moderate ($S=\pm 1$) is controlled by a reinforcement parameter $r \ge 0$. 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 $\beta$. 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 $\beta$, the two-network system reaches a consensus in the positive state (initial state of network $A$) when the reinforcement overcomes a crossover value $r^*(\beta)$, while a negative consensus happens for $r<r^*(\beta)$. In the $r-\beta$ phase space, the system displays a transition at a critical threshold $\beta_c$, from a coexistence of both orientations for $\beta<\beta_c$ to a dominance of one orientation for $\beta>\beta_c$. 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 $(r^*,\beta^*)$.
Edmilson Roque
Shared posts
Interacting social processes on interconnected networks. (arXiv:1604.07444v2 [physics.soc-ph] UPDATED)
A model to identify urban traffic congestion hotspots in complex networks. (arXiv:1604.07728v2 [physics.soc-ph] UPDATED)
Traffic congestion is one of the most notable problems arising in worldwide urban areas, importantly compromising human mobility and air quality. Current technologies to sense real-time data about cities, and its open distribution for analysis, allow the advent of new approaches for improvement and control. Here, we propose an idealized model, the Microscopic Congestion Model, based on the critical phenomena arising in complex networks, that allows to analytically predict congestion hotspots in urban environments. Results on real cities' road networks, considering, in some experiments, real-traffic data, show that the proposed model is capable of identifying susceptible junctions that might become hotspots if mobility demand increases.
Connectivity disruption sparks explosive epidemic spreading. (arXiv:1604.07783v1 [physics.soc-ph])
We investigate the spread of an infection or other malfunction of cascading nature when a system component can recover only if it remains reachable from a functioning central component. We consider the susceptible-infected-susceptible model, typical of mathematical epidemiology, on a network. Infection spreads from infected to healthy nodes, with the addition that infected nodes can only recover when they remain connected to a predefined central node, through a path that contains only healthy nodes. In this system, clusters of infected nodes will absorb their noninfected interior because no path exists between the central node and encapsulated nodes. This gives rise to the simultaneous infection of multiple nodes. Interestingly, the system converges to only one of two stationary states: either the whole population is healthy or it becomes completely infected. This simultaneous cluster infection can give rise to discontinuous jumps of different sizes in the number of failed nodes. Larger jumps emerge at lower infection rates. The network topology has an important effect on the nature of the transition: we observed hysteresis for networks with dominating local interactions. Our model shows how local spread can abruptly turn uncontrollable when it disrupts connectivity at a larger spatial scale.
Epidemic extinction and control in heterogeneous networks. (arXiv:1604.07244v2 [nlin.AO] UPDATED)
We consider epidemic extinction in finite networks with broad variation in local connectivity. Generalizing the theory of large fluctuations to random networks with a given degree distribution, we are able to predict the most probable, or optimal, paths to extinction in various configurations, including truncated power-laws. We find that paths for heterogeneous networks follow a limiting form in which infection first decreases in low-degree nodes, which triggers a rapid extinction in high- degree nodes, and finishes with a residual low-degree extinction. The usefulness of the approach is further demonstrated through optimal control strategies that leverage finite-size fluctuations. Interestingly, we find that the optimal control is a mix of treating both high and low-degree nodes based on large-fluctuation theoretical predictions.
Connectivity disruption sparks explosive epidemic spreading
Author(s): L. Böttcher, O. Woolley-Meza, E. Goles, D. Helbing, and H. J. Herrmann
We investigate the spread of an infection or other malfunction of cascading nature when a system component can recover only if it remains reachable from a functioning central component. We consider the susceptible-infected-susceptible model, typical of mathematical epidemiology, on a network. Infect…
[Phys. Rev. E 93, 042315] Published Mon Apr 25, 2016
Collective frequency variation in network synchronization and reverse PageRank
Author(s): Per Sebastian Skardal, Dane Taylor, Jie Sun, and Alex Arenas
A wide range of natural and engineered phenomena rely on large networks of interacting units to reach a dynamical consensus state where the system collectively operates. Here we study the dynamics of self-organizing systems and show that for generic directed networks the collective frequency of the …
[Phys. Rev. E 93, 042314] Published Mon Apr 25, 2016
Traveling phase waves in asymmetric networks of noisy chaotic attractors. (arXiv:1604.06603v1 [nlin.CD])
We explore identical R\"ossler systems organized into two equally-sized groups, among which differing positive and negative in- and out-coupling strengths are allowed. Patterns of distinctly synchronized phase dynamics are observed, which coexist with chaotically evolving amplitudes. In particular, we report the emergence of traveling phase waves, i.e. states in which the oscillators settle on a new rhythm different from their own. We further elucidate our findings through phase-coupled R\"ossler systems, establishing a connection with the Kuramoto model. Together with the study of noise effects, our results suggest a promising new avenue towards the coexistence of chaotic, noisy and regular collective dynamics.
Synchronization in heterogeneous FitzHugh-Nagumo networks with hierarchical architecture. (arXiv:1604.06203v2 [nlin.AO] UPDATED)
We study synchronization in heterogeneous FitzHugh-Nagumo networks. It is well known that heterogeneities in the nodes hinder synchronization when becoming too large. Here, we develop a controller to counteract the impact of these heterogeneities. We first analyze the stability of the equilibrium point in a ring network of heterogeneous nodes. We then derive a sufficient condition for synchronization in the absence of control. Based on these results we derive the controller providing synchronization for parameter values where synchronization without control is absent. We demonstrate our results in networks with different topologies. Particular attention is given to hierarchical (fractal) topologies, which are relevant for the architecture of the brain.
Experimental demonstration of revival of oscillations from death in coupled nonlinear oscillators
We experimentally demonstrate that a processing delay, a finite response time, in the coupling can revoke the stability of the stable steady states, thereby facilitating the revival of oscillations in the same parameter space where the coupled oscillators suffered the quenching of oscillation. This phenomenon of reviving of oscillations is demonstrated using two different prototype electronic circuits. Further, the analytical critical curves corroborate that the spread of the parameter space with stable steady state is diminished continuously by increasing the processing delay. Finally, the death state is completely wiped off above a threshold value by switching the stability of the stable steady state to retrieve sustained oscillations in the same parameter space. The underlying dynamical mechanism responsible for the decrease in the spread of the stable steady states and the eventual reviving of oscillation as a function of the processing delay is explained using analytical results.
Universality classes of the generalized epidemic process on random networks
Author(s): Kihong Chung, Yongjoo Baek, Meesoon Ha, and Hawoong Jeong
We present a self-contained discussion of the universality classes of the generalized epidemic process (GEP) on Poisson random networks, which is a simple model of social contagions with cooperative effects. These effects lead to rich phase transitional behaviors that include continuous and disconti…[Phys. Rev. E] Published Tue Apr 19, 2016
Analytically tractable studies of traveling waves of activity in integrate-and-fire neural networks
Author(s): Jie Zhang and Remus Osan
In contrast to other large-scale network models for propagation of electrical activity in neural tissue that have no analytical solutions for their dynamics, we show that for a specific class of integrate and fire neural networks the acceleration depends quadratically on the instantaneous speed of t…[Phys. Rev. E] Published Tue Apr 12, 2016
Chimera-type states induced by local coupling
Author(s): M. G. Clerc, S. Coulibaly, M. A. Ferré, M. A. García-Ñustes, and R. G. Rojas
Coupled oscillators can exhibit complex self-organization behavior such as phase turbulence, spatiotemporal intermittency and chimera states. The latter corresponds to a coexistence of coherent and incoherent states apparently promoted by nonlocal or global coupling. Here we investigate the existenc…[Phys. Rev. E] Published Tue Apr 12, 2016
Collective frequency variation in network synchronization and reverse PageRank
Author(s): Per Sebastian Skardal, Dane Taylor, Jie Sun, and Alex Arenas
A wide range of natural and engineered phenomena rely on large networks of interacting units to reach a dynamical consensus state where the system collectively operates. Here we study the dynamics of self-organizing systems and show that for generic directed networks the collective frequency of the …[Phys. Rev. E] Published Tue Apr 12, 2016
Master stability islands for amplitude death in networks of delay-coupled oscillators
Author(s): Stanley R. Huddy and Jie Sun
This paper presents a master stability function (MSF) approach for analyzing the stability of amplitude death (AD) in networks of delay-coupled oscillators. Unlike the familiar MSFs for instantaneously coupled networks, which typically have a single input encoding for the effects of the eigenvalues …[Phys. Rev. E] Published Tue Apr 12, 2016
Symmetry-broken states on networks of coupled oscillators
Author(s): Xin Jiang and Daniel M. Abrams
When identical oscillators are coupled together in a network, dynamical steady states are often assumed to reflect network symmetries. Here we show that alternative persistent states may also exist that break the symmetries of the underlying coupling network. We further show that these symmetry-brok…[Phys. Rev. E] Published Mon Apr 11, 2016
Connectivity disruption sparks explosive epidemic spreading
Author(s): L. Böttcher, O. Woolley-Meza, E. Goles, D. Helbing, and H. J. Herrmann
We investigate the spread of an infection or other malfunction of cascading nature when a system component can recover only if it remains reachable from a functioning central component. We consider the Susceptible-Infected-Susceptible (SIS) model, typical of mathematical epidemiology, on a network. …[Phys. Rev. E] Published Thu Apr 07, 2016
Epidemic spreading with activity-driven awareness diffusion on multiplex network
There has been growing interest in exploring the interplay between epidemic spreading with human response, since it is natural for people to take various measures when they become aware of epidemics. As a proper way to describe the multiple connections among people in reality, multiplex network, a set of nodes interacting through multiple sets of edges, has attracted much attention. In this paper, to explore the coupled dynamical processes, a multiplex network with two layers is built. Specifically, the information spreading layer is a time varying network generated by the activity driven model, while the contagion layer is a static network. We extend the microscopic Markov chain approach to derive the epidemic threshold of the model. Compared with extensive Monte Carlo simulations, the method shows high accuracy for the prediction of the epidemic threshold. Besides, taking different spreading models of awareness into consideration, we explored the interplay between epidemic spreading with awareness spreading. The results show that the awareness spreading can not only enhance the epidemic threshold but also reduce the prevalence of epidemics. When the spreading of awareness is defined as susceptible-infected-susceptible model, there exists a critical value where the dynamical process on the awareness layer can control the onset of epidemics; while if it is a threshold model, the epidemic threshold emerges an abrupt transition with the local awareness ratio α approximating 0.5. Moreover, we also find that temporal changes in the topology hinder the spread of awareness which directly affect the epidemic threshold, especially when the awareness layer is threshold model. Given that the threshold model is a widely used model for social contagion, this is an important and meaningful result. Our results could also lead to interesting future research about the different time-scales of structural changes in multiplex networks.
The noisy voter model on complex networks. (arXiv:1602.06935v3 [physics.soc-ph] UPDATED)
We propose a new analytical method to study stochastic, binary-state models on complex networks. Moving beyond the usual mean-field theories, this alternative approach is based on the introduction of an annealed approximation for uncorrelated networks, allowing to deal with the network structure as parametric heterogeneity. As an illustration, we study the noisy voter model, a modification of the original voter model including random changes of state. The proposed method is able to unfold the dependence of the model not only on the mean degree (the mean-field prediction) but also on more complex averages over the degree distribution. In particular, we find that the degree heterogeneity ---variance of the underlying degree distribution--- has a strong influence on the location of the critical point of a noise-induced, finite-size transition occurring in the model, on the local ordering of the system, and on the functional form of its temporal correlations. Finally, we show how this latter point opens the possibility of inferring the degree heterogeneity of the underlying network by observing only the aggregate behavior of the system as a whole, an issue of interest for systems where only macroscopic, population level variables can be measured.
The noisy voter model on complex networks
The noisy voter model on complex networks
Scientific Reports, Published online: 20 April 2016; doi:10.1038/srep24775
Anderson localization on random regular graphs. (arXiv:1604.05353v2 [cond-mat.dis-nn] UPDATED)
A numerical study of Anderson transition on random regular graphs (RRG) with diagonal disorder is performed. The problem can be described as a tight-binding model on a lattice with N sites that is locally a tree with constant connectivity. In certain sense, the RRG ensemble can be seen as infinite-dimensional ($d\to\infty$) cousin of Anderson model in d dimensions. We focus on the delocalized side of the transition and stress the importance of finite-size effects. We show that the data can be interpreted in terms of the finite-size crossover from small ($N\ll N_c$) to large ($N\gg N_c$) system, where $N_c$ is the correlation volume diverging exponentially at the transition. A distinct feature of this crossover is a nonmonotonicity of the spectral and wavefunction statistics, which is related to properties of the critical phase in the studied model and renders the finite-size analysis highly non-trivial. Our results support an analytical prediction that states in the delocalized phase (and at $N\gg N_c$) are ergodic in the sense that their inverse participation ratio scales as $1/N$.
Algebraic bounds for heterogeneous site percolation on directed and undirected graphs. (arXiv:1505.03963v4 [math-ph] UPDATED)
We analyze heterogeneous site percolation and the corresponding uniqueness transition on directed and undirected graphs, by constructing upper bounds on the in-/out-cluster susceptibilities and the vertex connectivity function. We give separate bounds on finite and infinite (di)graphs, and analyze the convergence in the infinite graph limit. We also discuss the transition associated with proliferation of self-avoiding cycles in relation to the uniqueness transition. The bounds are formulated in terms of the appropriately weighted adjacency and non-backtracking (Hashimoto) operators associated with the graphs.
The timescales of global surface-ocean connectivity
Article
The adaptive capabilities of planktonic communities to climate change remain uncertain. Here, using Lagrangian particle tracking and network theory, the authors show that surface ocean currents can navigate the globe within 10 years, suggesting that marine plankton may keep pace with climate change.
Nature Communications doi: 10.1038/ncomms11239
Authors: Bror F. Jönsson, James R. Watson
Threshold models of cascades in large-scale networks. (arXiv:1604.05490v1 [cs.SI])
The spread of new beliefs, behaviors, conventions, norms, and technologies in social and economic networks are often driven by cascading mechanisms, and so are contagion dynamics in financial networks. Global behaviors generally emerge from the interplay between the structure of the interconnection topology and the local agents' interactions. We focus on the Linear Threshold Model (LTM) of cascades first introduced by Granovetter (1978). This can be interpreted as the best response dynamics in a network game whereby agents choose strategically between two actions and their payoff is an increasing function of the number of their neighbors choosing the same action. Each agent is equipped with an individual threshold representing the number of her neighbors who must have adopted a certain action for that to become the agent's best response. We analyze the LTM dynamics on large-scale networks with heterogeneous agents. Through a local mean-field approach, we obtain a nonlinear, one-dimensional, recursive equation that approximates the evolution of the LTM dynamics on most of the networks of a given size and distribution of degrees and thresholds. Specifically, we prove that, on all but a fraction of networks with given degree and threshold statistics that is vanishing as the network size grows large, the actual fraction of adopters of a given action in the LTM dynamics is arbitrarily close to the output of the aforementioned recursion. We then analyze the dynamic behavior of this recursion and its bifurcations from a dynamical systems viewpoint. Applications of our findings to some real network testbeds show good adherence of the theoretical predictions to numerical simulations.
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Simple and accurate analytical calculation of shortest path lengths. (arXiv:1604.05521v1 [physics.soc-ph])
We present an analytical approach to calculating the distribution of shortest paths lengths (also called intervertex distances, or geodesic paths) between nodes in unweighted undirected networks. We obtain very accurate results for synthetic random networks with specified degree distribution (the so-called configuration model networks). Our method allows us to accurately predict the distribution of shortest path lengths on real-world networks using their degree distribution, or joint degree-degree distribution. Compared to some other methods, our approach is simpler and yields more accurate results. In order to obtain the analytical results, we use the analogy between an infection reaching a node in $n$ discrete time steps (i.e., as in the susceptible-infected epidemic model) and that node being at a distance $n$ from the source of the infection.
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Suppression of phase synchronisation in network based on cat's brain
We have studied the effects of perturbations on the cat's cerebral cortex. According to the literature, this cortex structure can be described by a clustered network. This way, we construct a clustered network with the same number of areas as in the cat matrix, where each area is described as a sub-network with a small-world property. We focus on the suppression of neuronal phase synchronisation considering different kinds of perturbations. Among the various controlling interventions, we choose three methods: delayed feedback control, external time-periodic driving, and activation of selected neurons. We simulate these interventions to provide a procedure to suppress undesired and pathological abnormal rhythms that can be associated with many forms of synchronisation. In our simulations, we have verified that the efficiency of synchronisation suppression by delayed feedback control is higher than external time-periodic driving and activation of selected neurons of the cat's cerebral cortex with the same coupling strengths.
Message passing theory for percolation models on multiplex networks with link overlap. (arXiv:1604.05175v2 [physics.soc-ph] UPDATED)
Multiplex networks describe a large variety of complex systems including infrastructures, transportation networks and biological systems. Most of these networks feature a significant link overlap. It is therefore of particular importance to characterize the mutually connected giant component in these networks. Here we provide a message passing theory for characterizing the percolation transition in multiplex networks with link overlap and an arbitrary number of layers $M$. Specifically we propose and compare two message passing algorithms, that generalize the algorithm widely used to study the percolation transition in multiplex networks without link overlap. The first algorithm describes a directed percolation transition and admits an epidemic spreading interpretation. The second algorithm describes the emergence of the mutually connected giant component, that is the percolation transition, but does not preserve the epidemic spreading interpretation. We obtain the phase diagrams for the percolation and directed percolation transition in simple representative cases. We demonstrate that for the same multiplex network structure, in which the directed percolation transition has non-trivial tricritical points, the percolation transition has a discontinuous phase transition, with the exception of the trivial case in which all the layers completely overlap.
Collective dynamics of identical phase oscillators with high-order coupling. (arXiv:1604.04816v1 [nlin.AO])
In this paper, we propose a framework to investigate the collective dynamics in ensembles of globally coupled phase oscillators when higher-order modes dominate the coupling. The spatiotemporal properties of the attractors in various regions of parameter space are analyzed. Furthermore, a detailed linear stability analysis proves that the stationary symmetric distribution is only neutrally stable in the marginal regime which stems from the generalized time-reversal symmetry. Moreover, the critical parameters of the transition among various regimes are determined analytically by both the Ott-Antonsen method and linear stability analysis, the transient dynamics are further revealed in terms of the characteristic curves method. Finally, for the more general initial condition the symmetric dynamics could be reduced to a rigorous three-dimensional manifold which shows that the neutrally stable chaos could also occur in this model for particular parameter. Our theoretical analysis and numerical results are consistent with each other, which can help us understand the dynamical properties in general system with higher-order harmonics couplings.
Correlation networks from flows. The case of forced and time-dependent advection-diffusion dynamics. (arXiv:1604.04922v1 [physics.flu-dyn])
Complex network theory provides an elegant and powerful framework to statistically investigate different types of systems such as society, brain or the structure of local and long-range dynamical interrelationships in the climate system. Network links in climate networks typically imply information, mass or energy exchange. However, the specific connection between oceanic or atmospheric flows and the climate network's structure is still unclear. We propose a theoretical approach for verifying relations between the correlation matrix and the climate network measures, generalizing previous studies and overcoming the restriction to stationary flows. Our methods are developed for correlations of a scalar quantity (temperature, for example) which satisfies an advection-diffusion dynamics in the presence of forcing and dissipation. Our approach reveals that correlation networks are not sensitive to steady sources and sinks and the profound impact of the signal decay rate on the network topology. We illustrate our results with calculations of degree and clustering for a meandering flow resembling a geophysical ocean jet.
Controlling synchronous patterns in complex networks
Author(s): Weijie Lin, Huawei Fan, Ying Wang, Heping Ying, and Xingang Wang
Although the set of permutation symmetries of a complex network could be very large, few of them give rise to stable synchronous patterns. Here we present a general framework and develop techniques for controlling synchronization patterns in complex network of coupled chaotic oscillators. Specifical…
[Phys. Rev. E 93, 042209] Published Mon Apr 18, 2016
Network-scale effect on synchronizability of fully coupled network with connection delay
Network-scaleeffect on synchronizability of fully coupled network with connection delay is investigated in this paper. The master stability function, which governs the stability of synchronizationmanifold, is first obtained by separating the synchronizationmanifold direction from other transverse directions. Then, by introducing a new time variable in the master stability function, it is shown the effect of connection delay can be weakened with the increase of network scale, and thus, in contrast to the situation without connection delay, large network scale is more positive to the synchronizability of fully coupled network with connection delay. Those findings are confirmed by the studies on two specific networks with nodes of typical nonlinear dynamical systems.