Studying power-grid synchronization with incremental refinement of model heterogeneity.

The dynamics of electric power systems are widely studied through the phase synchronization of oscillators, typically with the use of the Kuramoto equation. While there are numerous well-known order parameters to characterize these dynamics, shortcoming of these metrics are also recognized. To capture all transitions from phase disordered states over phase locking to fully synchronized systems, new metrics were proposed and demonstrated on homogeneous models.

Frustrated Synchronization of the Kuramoto Model on Complex Networks.

We present a synchronization transition study of the locally coupled Kuramoto model on extremely large graphs. We compare regular 405 and 1004 lattice results with those of 12,0002 lattice substrates with power-law decaying long links (ll). The latter heterogeneous network exhibits ds>4 spectral dimensions.

Chimera-like states in neural networks and power systems.

Partial, frustrated synchronization, and chimera-like states are expected to occur in Kuramoto-like models if the spectral dimension of the underlying graph is low: ds<4. We provide numerical evidence that this really happens in the case of the high-voltage power grid of Europe (ds<2), a large human connectome (KKI113) and in the case of the largest, exactly known brain network corresponding to the fruit-fly (FF) connectome (ds<4), even though their graph dimensions are much higher, i.e.

Scaling laws of failure dynamics on complex networks.

The topology of the network of load transmitting connections plays an essential role in the cascading failure dynamics of complex systems driven by the redistribution of load after local breakdown events. In particular, as the network structure is gradually tuned from regular to completely random a transition occurs from the localized to mean field behavior of failure spreading. Based on finite size scaling in the fiber bundle model of failure phenomena, here we demonstrate that outside the localized regime, the load bearing capacity and damage tolerance on the macro-scale, and the statistics of clusters of failed nodes on the micro-scale obey scaling laws with exponents which depend on the topology of the load transmission network and on the degree of disorder of the strength of nodes.

Source identification via contact tracing in the presence of asymptomatic patients.

Inferring the source of a diffusion in a large network of agents is a difficult but feasible task, if a few agents act as sensors revealing the time at which they got hit by the diffusion. One of the main limitations of current source identification algorithms is that they assume full knowledge of the contact network, which is rarely the case, especially for epidemics, where the source is called patient zero. Inspired by recent implementations of contact tracing algorithms, we propose a new framework, which we call Source Identification via Contact Tracing Framework (SICTF).

Critical behavior of the diffusive susceptible-infected-recovered model.

The critical behavior of the nondiffusive susceptible-infected-recovered model on lattices had been well established in virtue of its duality symmetry. By performing simulations and scaling analyses for the diffusive variant on the two-dimensional lattice, we show that diffusion for all agents, while rendering this symmetry destroyed, constitutes a singular perturbation that induces asymptotically distinct dynamical and stationary critical behavior from the nondiffusive model. In particular, the manifested crossover behavior in the effective mean-square radius exponents reveals that slow crossover behavior in general diffusive multispecies reaction systems may be ascribed to the interference of multiple length scales and timescales at early times.

Synchronization Transition of the Second-Order Kuramoto Model on Lattices.

The second-order Kuramoto equation describes the synchronization of coupled oscillators with inertia, which occur, for example, in power grids. On the contrary to the first-order Kuramoto equation, its synchronization transition behavior is significantly less known. In the case of Gaussian self-frequencies, it is discontinuous, in contrast to the continuous transition for the first-order Kuramoto equation.

Synchronization dynamics on power grids in Europe and the United States.

Dynamical simulation of the cascade failures on the Europe and United States (U.S.) high-voltage power grids has been done via solving the second-order Kuramoto equation.

Erratum: Nonuniversal power-law dynamics of susceptible infected recovered models on hierarchical modular networks [Phys. Rev. E 103, 062112 (2021)].

This corrects the article DOI: 10.1103/PhysRevE.103.

Switchover phenomenon induced by epidemic seeding on geometric networks.

It is a fundamental question in disease modeling how the initial seeding of an epidemic, spreading over a network, determines its final outcome. One important goal has been to find the seed configuration, which infects the most individuals. Although the identified optimal configurations give insight into how the initial state affects the outcome of an epidemic, they are unlikely to occur in real life.

Nonuniversal power-law dynamics of susceptible infected recovered models on hierarchical modular networks.

Power-law (PL) time-dependent infection growth has been reported in many COVID-19 statistics. In simple susceptible infected recovered (SIR) models, the number of infections grows at the outbreak as I(t)∝t^{d-1} on d-dimensional Euclidean lattices in the endemic phase, or it follows a slower universal PL at the critical point, until finite sizes cause immunity and a crossover to an exponential decay. Heterogeneity may alter the dynamics of spreading models, and spatially inhomogeneous infection rates can cause slower decays, posing a threat of a long recovery from a pandemic.

Power-Law Distributions of Dynamic Cascade Failures in Power-Grid Models.

Power-law distributed cascade failures are well known in power-grid systems. Understanding this phenomena has been done by various DC threshold models, self-tuned at their critical point. Here, we attempt to describe it using an AC threshold model, with a second-order Kuramoto type equation of motion of the power-flow.

Critical synchronization dynamics of the Kuramoto model on connectome and small world graphs.

The hypothesis, that cortical dynamics operates near criticality also suggests, that it exhibits universal critical exponents which marks the Kuramoto equation, a fundamental model for synchronization, as a prime candidate for an underlying universal model. Here, we determined the synchronization behavior of this model by solving it numerically on a large, weighted human connectome network, containing 836733 nodes, in an assumed homeostatic state. Since this graph has a topological dimension d < 4, a real synchronization phase transition is not possible in the thermodynamic limit, still we could locate a transition between partially synchronized and desynchronized states.

Robustness of Griffiths effects in homeostatic connectome models.

I provide numerical evidence for the robustness of the Griffiths phase (GP) reported previously in dynamical threshold model simulations on a large human brain network with N=836733 connected nodes. The model, with equalized network sensitivity, is extended in two ways: introduction of refractory states or by randomized time-dependent thresholds. The nonuniversal power-law dynamics in an extended control parameter region survives these modifications for a short refractory state and weak disorder.

Heterogeneity effects in power grid network models.

We have compared the phase synchronization transition of the second-order Kuramoto model on two-dimensional (2D) lattices and on large, synthetic power grid networks, generated from real data. The latter are weighted, hierarchical modular networks. Due to the inertia the synchronization transitions are of first-order type, characterized by fast relaxation and hysteresis by varying the global coupling parameter K.

Griffiths phases in infinite-dimensional, non-hierarchical modular networks.

Griffiths phases (GPs), generated by the heterogeneities on modular networks, have recently been suggested to provide a mechanism, rid of fine parameter tuning, to explain the critical behavior of complex systems. One conjectured requirement for systems with modular structures was that the network of modules must be hierarchically organized and possess finite dimension. We investigate the dynamical behavior of an activity spreading model, evolving on heterogeneous random networks with highly modular structure and organized non-hierarchically.

Critical dynamics on a large human Open Connectome network.

Extended numerical simulations of threshold models have been performed on a human brain network with N=836733 connected nodes available from the Open Connectome Project. While in the case of simple threshold models a sharp discontinuous phase transition without any critical dynamics arises, variable threshold models exhibit extended power-law scaling regions. This is attributed to fact that Griffiths effects, stemming from the topological or interaction heterogeneity of the network, can become relevant if the input sensitivity of nodes is equalized.

Universality of (2+1)-dimensional restricted solid-on-solid models.

Extensive dynamical simulations of restricted solid-on-solid models in D=2+1 dimensions have been done using parallel multisurface algorithms implemented on graphics cards. Numerical evidence is presented that these models exhibit Kardar-Parisi-Zhang surface growth scaling, irrespective of the step heights N. We show that by increasing N the corrections to scaling increase, thus smaller step-sized models describe better the asymptotic, long-wave-scaling behavior.

The topology of large Open Connectome networks for the human brain.

The structural human connectome (i.e. the network of fiber connections in the brain) can be analyzed at ever finer spatial resolution thanks to advances in neuroimaging.

Griffiths effects of the susceptible-infected-susceptible epidemic model on random power-law networks.

We provide numerical evidence for slow dynamics of the susceptible-infected-susceptible model evolving on finite-size random networks with power-law degree distributions. Extensive simulations were done by averaging the activity density over many realizations of networks. We investigated the effects of outliers in both highly fluctuating (natural cutoff) and nonfluctuating (hard cutoff) most connected vertices.

Griffiths phases and localization in hierarchical modular networks.

We study variants of hierarchical modular network models suggested by Kaiser and Hilgetag [ Front. in Neuroinform., 4 (2010) 8] to model functional brain connectivity, using extensive simulations and quenched mean-field theory (QMF), focusing on structures with a connection probability that decays exponentially with the level index.

Localization transition, Lifschitz tails, and rare-region effects in network models.

Effects of heterogeneity in the suspected-infected-susceptible model on networks are investigated using quenched mean-field theory. The emergence of localization is described by the distributions of the inverse participation ratio and compared with the rare-region effects appearing in simulations and in the Lifschitz tails. The latter, in the linear approximation, is related to the spectral density of the Laplacian matrix and to the time dependent order parameter.

Slow, bursty dynamics as a consequence of quenched network topologies.

Bursty dynamics of agents is shown to appear at criticality or in extended Griffiths phases, even in case of Poisson processes. I provide numerical evidence for a power-law type of intercommunication time distributions by simulating the contact process and the susceptible-infected-susceptible model. This observation suggests that in the case of nonstationary bursty systems, the observed non-Poissonian behavior can emerge as a consequence of an underlying hidden Poissonian network process, which is either critical or exhibits strong rare-region effects.

Aging of the (2+1)-dimensional Kardar-Parisi-Zhang model.

Extended dynamical simulations have been performed on a (2+1)-dimensional driven dimer lattice-gas model to estimate aging properties. The autocorrelation and the autoresponse functions are determined and the corresponding scaling exponents are tabulated. Since this model can be mapped onto the (2+1)-dimensional Kardar-Parisi-Zhang surface growth model, our results contribute to the understanding of the universality class of that basic system.

Spectral analysis and slow spreading dynamics on complex networks.

The susceptible-infected-susceptible (SIS) model is one of the simplest memoryless systems for describing information or epidemic spreading phenomena with competing creation and spontaneous annihilation reactions. The effect of quenched disorder on the dynamical behavior has recently been compared to quenched mean-field (QMF) approximations in scale-free networks. QMF can take into account topological heterogeneity and clustering effects of the activity in the steady state by spectral decomposition analysis of the adjacency matrix.