Author(s): Ernesto Estrada, Sandro Meloni, Matthew Sheerin, and Yamir Moreno
The use of network theory to model disease propagation on populations introduces important elements of reality to the classical epidemiological models. The use of random geometric graphs (RGG) is one of such network models that allows for the consideration of spatial properties on disease propagatio…[Phys. Rev. E] Published Tue Nov 08, 2016
Author(s): Debsankha Manik, Martin Rohden, Henrik Ronellenfitsch, Xiaozhu Zhang, Sarah Hallerberg, Dirk Witthaut, and Marc Timme
We introduce the concept of network susceptibilities quantifying the response of the collective dynamics of a network to small parameter changes. We distinguish two types of susceptibilities: vertex susceptibilities and edge susceptibilities, measuring the responses due to changes in the properties …[Phys. Rev. E] Published Tue Nov 08, 2016
Nature Physics. doi:10.1038/nphys3927
Authors: A. A. Awad, P. Dürrenfeld, A. Houshang, M. Dvornik, E. Iacocca, R. K. Dumas & J. Åkerman
Author(s): Shao-Peng Pang, Fei Hao, and Wen-Xu Wang
The robustness of controlling complex networks is significant in network science. In this paper, we focus on evaluating and analyzing the robustness of controlling edge dynamics in complex networks against node failure. Using three categories of all nodes to quantify the robustness, we find that the…
[Phys. Rev. E 94, 052310] Published Mon Nov 14, 2016
Author(s): Jinjie Zhu and Xianbin Liu
In the present paper, the locking phenomenon induced by distance-dependent delay in ring structured neuronal networks is investigated, wherein each neuron is modeled by a FitzHugh-Nagumo neuron. Through increasing the element time delay, the different spatiotemporal patterns are observed. By calcula…
[Phys. Rev. E 94, 052405] Published Mon Nov 14, 2016
Author(s): Can Xu, Jian Gao, Hairong Xiang, Wenjing Jia, Shuguang Guan, and Zhigang Zheng
{\bf \textcolor[rgb]{1.00,0.00,0.00}{Heterogeneous coupling patterns among interacting elements are ubiquitous in real systems ranging from physics, chemistry to biology communities, which have attracted much attention during \textcolor[rgb]{0.00,0.00,1.00}{ recent} years. In this paper, we extend t…[Phys. Rev. E] Published Thu Nov 10, 2016
Author(s): Sho Shirasaka, Wataru Kurebayashi, and Hiroya Nakao
Hybrid dynamical systems characterized by discrete switching of smooth dynamics have been used to model various rhythmic phenomena. However, the phase reduction theory, a fundamental framework for analyzing the synchronization of limit-cycle oscillations in rhythmic systems, has mostly been restrict…[Phys. Rev. E] Published Fri Nov 11, 2016
Chimera states are complex spatio-temporal patterns that consist of coexisting domains of coherent and incoherent dynamics. We study chimera states in a network of non-locally coupled Stuart-Landau oscillators. We investigate the impact of initial conditions in combination with non-local coupling. Based on an analytical argument, we show how the coupling phase and the coupling strength are linked to the occurrence of chimera states, flipped profiles of the mean phase velocity, and the transition from a phase- to an amplitude-mediated chimera state.
For a given minimum cost of the electricity dispatch, multiple equivalent dispatch solutions may exist. We explore the sensitivity of networks to these dispatch solutions and their impact on the vulnerability of the network to cascading failure blackouts. It is shown that, depending on the heterogeneity of the network structure, the blackout statistics can be sensitive to the dispatch solution chosen, with the clustering coefficient of the network being a key ingredient. We also investigate mechanisms or configurations that decrease discrepancies that can occur between the different dispatch solutions.
We generalize the diffusion-limited aggregation by issuing many randomly-walking particles, which stick to a cluster at the discrete time unit providing its growth. Using simple combinatorial arguments we determine probabilities of different growth scenarios and prove that the most probable evolution is governed by the deterministic Laplacian growth equation. A potential-theoretical analysis of the growth probabilities reveals connections with the tau-function of the integrable dispersionless limit of the two-dimensional Toda hierarchy, normal matrix ensembles, and the two-dimensional Dyson gas confined in a non-uniform magnetic field. We introduce the time-dependent Hamiltonian, which generates transitions between different classes of equivalence of closed curves, and prove the Hamiltonian structure of the interface dynamics. Finally, we propose a relation between probabilities of growth scenarios and the semi-classical limit of certain correlation functions of "light" exponential operators in the Liouville conformal field theory on a pseudosphere.
Chimera states, which consist of coexisting domains of coherent and incoherent parts, have been observed in a variety of systems. Most of previous works on chimera states have taken into account specific form of interaction between oscillators, for example sinusoidal coupling or diffusive coupling. Here, we investigate chimera dynamics in nonlocally coupled phase oscillators with biharmonic interaction. We find novel chimera states with features such as that oscillators in the same coherent cluster may split into two groups with a phase difference between them at around pi/2 and that oscillators in adjacent coherent clusters may have a phase difference close to pi/2. The different impacts of the coupling ranges in the first and the second harmonic interactions on chimera dynamics are investigated based on the synchronous dynamics in globally coupled phase oscillators. Our study suggests a new direction in the field of chimera dynamics.
Coupled oscillators were believed to exclusively exist in a state of synchrony or disorder until Kuramoto theoretically proved that the two states could coexist, called a chimera state, when portions of the population had a spatial dependent coupling. Recent work has demonstrated the spontaneous emergence of chimera states in an experiment involving mechanical oscillators coupled through a two platform swing. We constructed an experimental apparatus with three platforms that each contains a population of mechanical oscillators in order investigate the effects of a network symmetry on naturally arising chimera states. We considered in more detail the case of 15 metronomes per platform and observed that chimera states emerged as a broad range of parameters, namely, the metronomes' nominal frequency and the coupling strength between the platforms. A scalability study shows that chimera states no longer arise when the population size is reduced to three metronomes per platform. Furthermore, many chimera states are seen in the system when the coupling between platforms is asymmetric.
A new method (`explosive immunization' (EI)) is proposed for immunization and targeted destruction of networks. It combines the explosive percolation (EP) paradigm with the idea of maintaining a fragmented distribution of clusters. The ability of each node to block the spread of an infection (or to prevent the existence of a large cluster of connected nodes) is estimated by a score. The algorithm proceeds by first identifying low score nodes that should not be vaccinated/destroyed, analogously to the links selected in EP if they do not lead to large clusters. As in EP, this is done by selecting the worst node (weakest blocker) from a finite set of randomly chosen `candidates'. Tests on several real-world and model networks suggest that the method is more efficient and faster than any existing immunization strategy. Due to the latter property it can deal with very large networks.
Random planar graphs appear in a variety of context and it is important for many different applications to be able to characterize their structure. Local quantities fail to give interesting information and it seems that path-related measures are able to convey relevant information about the organization of these structures. In particular, nodes with a large betweenness centrality (BC) display non-trivial patterns, such as central loops. We first discuss empirical results for different random planar graphs and we then propose a toy model which allows us to discuss the condition for the emergence of non-trivial patterns such as central loops. This toy model is made of a star network with $N_b$ branches of size $n$ and links of weight $1$, superimposed to a loop at distance $\ell$ from the center and with links of weight $w$. We estimate for this model the BC at the center and on the loop and we show that the loop can be more central than the origin if $w<w_c$ where the threshold of this transition scales as $w_c\sim n/N_b$. In this regime, there is an optimal position of the loop that scales as $\ell_{opt}\sim N_b w/4$. This simple model sheds some light on the organization of these random structures and allows us to discuss the effect of randomness on the centrality of loops. In particular, it suggests that the number and the spatial extension of radial branches are the crucial ingredients that control the existence of central loops.
We show that amplitude chimeras in ring networks of Stuart-Landau oscillators with symmetry-breaking nonlocal coupling represent saddle-states in the underlying phase space of the network. Chimera states are composed of coexisting spatial domains of coherent and of incoherent oscillations. We calculate the Floquet exponents and the corresponding eigenvectors in dependence upon the coupling strength and range, and discuss the implications for the phase space structure. The existence of at least one positive real part of the Floquet exponents indicates an unstable manifold in phase space, which explains the nature of these states as long-living transients. Additionally, we find a Stuart-Landau network of minimum size $N=12$ exhibiting amplitude chimeras
We study a simple case of the susceptible-weakened-infected-removed model in regular random graphs in a situation where an epidemic starts from a finite fraction of initially infected nodes (seeds). Previous studies have shown that, assuming a single seed, this model exhibits a kind of discontinuous transition at a certain value of infection rate. Performing Monte Carlo simulations and evaluating approximate master equations, we find that the present model has two critical infection rates for the case with a finite seed fraction. At the first critical rate the system shows a percolation transition of clusters composed of removed nodes, and at the second critical rate, which is larger than the first one, a giant cluster suddenly grows and the order parameter jumps even though it has been already rising. Numerical evaluation of the master equations shows that such sudden epidemic spreading does occur if the degree of the underlying network is large and the seed fraction is small.
Rapidly mutating pathogens may be able to persist in the population and reach an endemic equilibrium by escaping hosts' acquired immunity. For such diseases, multiple biological, environmental and population-level mechanisms determine the dynamics of the outbreak, including pathogen's epidemiological traits (e.g. transmissibility, infectious period and duration of immunity), seasonality, interaction with other circulating strains and hosts' mixing and spatial fragmentation. Here, we study a susceptible-infected-recovered-susceptible model on a metapopulation where individuals are distributed in subpopulations connected via a network of mobility flows. Through extensive numerical simulations, we explore the phase space of pathogen's persistence and map the dynamical regimes of the pathogen following emergence. Our results show that spatial fragmentation and mobility play a key role in the persistence of the disease whose maximum is reached at intermediate mobility values. We describe the occurrence of different phenomena including local extinction and emergence of epidemic waves, and assess the conditions for large scale spreading. Findings are highlighted in reference to previous works and to real scenarios. Our work uncovers the crucial role of hosts' mobility on the ecological dynamics of rapidly mutating pathogens, opening the path for further studies on disease ecology in the presence of a complex and heterogeneous environment.
Author(s): R. Guevara Erra, D. M. Mateos, R. Wennberg, and J. L. Perez Velazquez
It is said that complexity lies between order and disorder. In the case of brain activity and physiology in general, complexity issues are being considered with increased emphasis. We sought to identify features of brain organization that are optimal for sensory processing, and that may guide the em…
[Phys. Rev. E 94, 052402] Published Tue Nov 08, 2016
Author(s): Pau Clusella, Peter Grassberger, Francisco J. Pérez-Reche, and Antonio Politi
A new method (“explosive immunization”) is proposed for immunization and targeted destruction of networks. It combines the explosive percolation (EP) paradigm with the idea of maintaining a fragmented distribution of clusters. The ability of each node to block the spread of an infection (or to preve…
[Phys. Rev. Lett. 117, 208301] Published Tue Nov 08, 2016
We demonstrate that chimera behavior can be observed in small networks consisting of three identical oscillators, with mutual all-to-all coupling. Three different types of chimeras, characterized by the coexistence of two coherent oscillators and one incoherent oscillator (i.e. rotating with another frequency) have been identified, where the oscillators show periodic (two types) and chaotic (one type) behaviors. Typical bifurcations at the transitions from full synchronization to chimera states and between different types of chimeras have been described. Parameter regions for the chimera states are obtained in the form of Arnold tongues, issued from a singular parameter point. Our analysis suggests that chimera states can be observed in small networks, relevant to various real-world systems.
Synchronization is the process of achieving identical dynamics among coupled identical units. If the units are different from each other, their dynamics cannot become identical; yet, after transients, there may emerge a functional relationship between them -- a phenomenon termed "generalized synchronization." Here, we show that the concept of transient uncoupling, recently introduced for synchronizing identical units, also supports generalized synchronization among nonidentical chaotic units. Generalized synchronization can be achieved by transient uncoupling even when it is impossible by regular coupling. We furthermore demonstrate that transient uncoupling stabilizes synchronization in the presence of common noise. Transient uncoupling works best if the units stay uncoupled whenever the driven orbit visits regions that are locally diverging in its phase space. Thus, to select a favorable uncoupling region, we propose an intuitive method that measures the local divergence at the phase points of the driven unit's trajectory by linearizing the flow and subsequently suppresses the divergence by uncoupling.
While a plethora of hypertext links exist on the Web, only a small amount of them are regularly clicked. Starting from this observation, we set out to study large-scale click data from Wikipedia in order to understand what makes a link successful. We systematically analyze effects of link properties on the popularity of links. By utilizing mixed-effects hurdle models supplemented with descriptive insights, we find evidence of user preference towards links leading to the periphery of the network, towards links leading to semantically similar articles, and towards links in the top and left-side of the screen. We integrate these findings as Bayesian priors into a navigational Markov chain model and by doing so successfully improve the model fits. We further adapt and improve the well-known classic PageRank algorithm that assumes random navigation by accounting for observed navigational preferences of users in a weighted variation. This work facilitates understanding navigational click behavior and thus can contribute to improving link structures and algorithms utilizing these structures.
The long-term evolution of epidemic processes depends crucially on the structure of contact networks. As empirical evidence indicates that human populations exhibit strong community organization, we investigate here how such mesoscopic configurations affect the likelihood of epidemic recurrence. Through numerical simulations on real social networks and theoretical arguments using spectral methods, we demonstrate that highly contagious diseases that would have otherwise died out rapidly can persist indefinitely for an optimal range of modularity in contact networks.
Author(s): Yuki Izumida, Hiroshi Kori, and Udo Seifert
We derive a concise and general expression of the energy dissipation rate for coupled oscillators rotating on circular trajectories by unifying the nonequilibrium aspects with the nonlinear dynamics via stochastic thermodynamics. In the framework of phase oscillator models, it is known that the even…[Phys. Rev. E] Published Mon Nov 07, 2016
Author(s): Bastian Pietras, Nicolás Deschle, and Andreas Daffertshofer
Populations of oscillators can display a variety of synchronization patterns depending on the oscillators' intrinsic coupling and the coupling between them. We consider two coupled symmetric (sub)populations with unimodal frequency distributions. If internal and external coupling strengths are ident…
[Phys. Rev. E 94, 052211] Published Wed Nov 09, 2016
We studied the phenomenon of chimera states in networks of non–locally coupled externally excited oscillators. Units of the considered networks are bi–stable, having two co–existing attractors of different types (chaotic and periodic). The occurrence of chimeras is discussed, and the influence of coupling radius and coupling strength on their co–existence is analyzed (including typical bifurcation scenarios). We present a statistical analysis and investigate sensitivity of the probability of observing chimeras to the initial conditions and parameter values. Due to the fact that each unit of the considered networks is individually excited, we study the influence of the excitation failure on stability of observed states. Typical transitions are shown, and changes in network's dynamics are discussed. We analyze systems of coupled van der Pol–Duffing oscillators and the Duffing ones. Described chimera states are robust as they are observed in the wide regions of parameter values, as well as in other networks of coupled forced oscillators.
Systems with non-linear dynamics frequently exhibit emergent system behavior, which is important to find and specify rigorously to understand the nature of the modeled phenomena. Through this analysis, it is possible to characterize phenomena such as how systems assemble or dissipate and what behaviors lead to specific final system configurations. Agent Based Modeling (ABM) is one of the modeling techniques used to study the interaction dynamics between a system's agents and its environment. Although the methodology of ABM construction is well understood and practiced, there are no computational, statistically rigorous, comprehensive tools to evaluate an ABM's execution. Often, a human has to observe an ABM's execution in order to analyze how the ABM functions, identify the emergent processes in the agent's behavior, or study a parameter's effect on the system-wide behavior. This paper introduces a new statistically based framework to automatically analyze agents' behavior, identify common system-wide patterns, and record the probability of agents changing their behavior from one pattern of behavior to another. We use network based techniques to analyze the landscape of common behaviors in an ABM's execution. Finally, we test the proposed framework with a series of experiments featuring increasingly emergent behavior. The proposed framework will allow computational comparison of ABM executions, exploration of a model's parameter configuration space, and identification of the behavioral building blocks in a model's dynamics.