Author(s): André Röhm, Fabian Böhm, and Kathy Lüdge
We present results obtained for a network of four delay-coupled lasers modeled by Lang-Kobayashi–type equations. We find small chimera states consisting of a pair of synchronized lasers and two unsynchronized lasers. One class of these small chimera states can be understood as intermediate steps on …
[Phys. Rev. E 94, 042204] Published Wed Oct 05, 2016
Rumor models consider that information transmission occurs with the same probability between each pair of nodes. However, this assumption is not observed in social networks, which contain influential spreaders. To overcome this limitation, we assume that central individuals have a higher capacity of convincing their neighbors than peripheral subjects. By extensive numerical simulations we find that the spreading is improved in scale-free networks when the transmission probability is proportional to PageRank, degree, and betweenness centrality. In addition, the results suggest that the spreading can be controlled by adjusting the transmission probabilities of the most central nodes. Our results provide a conceptual framework for understanding the interplay between rumor propagation and heterogeneous transmission in social networks.
Complex systems are characterized by specific time-dependent interactions among their many constituents. As a consequence they often manifest rich, non-trivial and unexpected behavior. Examples arise both in the physical and non-physical world. The study of complex systems forms a new interdisciplinary research area that cuts across physics, biology, ecology, economics, sociology, and the humanities. In this paper we review the essence of complex systems from a physicist's point of view, and try to clarify what makes them conceptually different from systems that are traditionally studied in physics. Our goal is to demonstrate how the dynamics of such systems may be conceptualized in quantitative and predictive terms by extending notions from statistical physics and how they can often be captured in a framework of co-evolving multiplex network structures. We mention three areas of complex-systems science that are currently studied extensively, the science of cities, dynamics of societies, and the representation of texts as evolutionary objects. We discuss why these areas form complex systems in the above sense. We argue that there exists plenty of new land for physicists to explore and that methodical and conceptual progress is needed most.
Failure, damage spread and recovery crucially underlie many spatially embedded networked systems ranging from transportation structures to the human body. Here we study the interplay between spontaneous damage, induced failure and recovery in both embedded and non-embedded networks. In our model the network's components follow three realistic processes that capture these features: (i) spontaneous failure of a component independent of the neighborhood (internal failure), (ii) failure induced by failed neighboring nodes (external failure) and (iii) spontaneous recovery of a component.We identify a metastable domain in the global network phase diagram spanned by the model's control parameters where dramatic hysteresis effects and random switching between two coexisting states are observed. The loss of predictability due to these effects depend on the characteristic link length of the embedded system. For the Euclidean lattice in particular, hysteresis and switching only occur in an extremely narrow region of the parameter space compared to random networks. We develop a unifying theory which links the dynamics of our model to contact processes. Our unifying framework may help to better understand predictability and controllability in spatially embedded and random networks where spontaneous recovery of components can mitigate spontaneous failure and damage spread in the global network.
A common way of classifying network connectivity is the association of the nodal degree distribution to specific probability distribution models. During the last decades, researchers classified many networks using the Poisson or Pareto distributions. Urban infrastructures, like transportation (railways, roads, etc.) and distribution (gas, water, energy, etc.) systems, are peculiar networks strongly constrained by spatial characteristics of the environment where they are constructed. Consequently, the nodal degree of such networks spans very small ranges not allowing a reliable classification using the nodal degree distribution. In order to overcome this problem, we here (i) define the neighborhood degree, equal to the sum of the nodal degrees of the nearest topological neighbors, the adjacent nodes and (ii) propose to use neighborhood degree to classify infrastructure networks. Such neighborhood degree spans a wider range of degrees than the standard one allowing inferring the probabilistic model in a more reliable way, from a statistical standpoint. In order to test our proposal, we here analyze twenty-two real water distribution networks, built in different environments, demonstrating that the Poisson distribution generally models very well their neighborhood degree distributions. This result seems consistent with the less reliable classification achievable with the scarce information using the standard nodal degree distribution.
Nature Physics 12, 901 (2016). doi:10.1038/nphys3865
Authors: Manlio De Domenico, Clara Granell, Mason A. Porter & Alex Arenas
We present a case study of how topology can affect synchronization. Specifically, we consider arrays of phase oscillators coupled in a ring or a chain topology. Each ring is perfectly matched to a chain with the same initial conditions and the same random natural frequencies. The only difference is their boundary conditions: periodic for a ring, and open for a chain. For both topologies, stable phase-locked states exist if and only if the spread or "width" of the natural frequencies is smaller than a critical value called the locking threshold (which depends on the boundary conditions and the particular realization of the frequencies). The central question is whether a ring synchronizes more readily than a chain. We show that it usually does, but not always. Rigorous bounds are derived for the ratio between the locking thresholds of a ring and its matched chain, for a variant of the Kuramoto model that also includes a wider family of models.
A collective chaotic phase with power law scaling of activity events is observed in a disordered mean field network of purely excitatory leaky integrate-and-fire neurons with short-term synaptic plasticity. The dynamical phase diagram exhibits two transitions from quasi-synchronous and asynchronous regimes to the nontrivial, collective, bursty regime with avalanches. In the homogeneous case without disorder, the system synchronizes and the bursty behavior is reflected into a doubling-period transition to chaos for a two dimensional discrete map. Numerical simulations show that the bursty chaotic phase with avalanches exhibits a spontaneous emergence of time correlations and enhanced Kolmogorov complexity. Our analysis reveals a mechanism for the generation of irregular avalanches that emerges from the combination of disorder and deterministic underlying chaotic dynamics.
Nature Physics 12, 889 (2016). doi:10.1038/nphys3923
Nature Physics now requires its published papers to include information on whether and how their underlying data are accessible to others.
The Ott-Antonsen (OA) ansatz [Ott and Antonsen, Chaos 18, 037113 (2008); Chaos 19, 023117 (2009)] has been widely used to describe large systems of coupled phase oscillators. If the coupling is sinusoidal and if the phase dynamics does not depend on the specific oscillator, then the macroscopic behavior of the systems can be fully described by a low-dimensional dynamics. Does the corresponding manifold remain attractive when introducing an intrinsic dependence between an oscillator's phase and its dynamics by additional, oscillator specific parameters? To answer this, we extended the OA ansatz and proved that parameter-dependent oscillatory systems converge to the OA manifold given certain conditions. Our proof confirms recent numerical findings that already hinted at this convergence. Furthermore, we offer a thorough mathematical underpinning for networks of so-called theta neurons, where the OA ansatz has just been applied. In a final step, we extend our proof by allowing for time-dependent and multi-dimensional parameters as well as for network topologies other than global coupling. This renders the OA ansatz an excellent starting point for the analysis of a broad class of realistic settings.
Nature Physics. doi:10.1038/nphys3929
Authors: C. J. Olson Reichhardt & C. Reichhardt
Simple models have given us surprising insight into how animals flock, but most assume they do so through a homogeneous landscape. Colloidal experiments now suggest that a little disorder can have unexpected — and spectacular — effects.
Author(s): Annabelle Shaffer, Allison L. Harris, Rosangela Follmann, and Epaminondas Rosa, Jr.
Here we investigate transitions occurring in the dynamical states of pairs of distinct neurons electrically coupled, with one neuron tonic and the other bursting. Depending on the dynamics of the individual neurons, and for strong enough coupling, they synchronize either in a tonic or a bursting reg…
[Phys. Rev. E 94, 042301] Published Mon Oct 03, 2016
Author(s): Margarita Kovaleva, Valery Pilipchuk, and Leonid Manevitch
The present work follows our previous study dealing with a new type of synchronization in a system of two weakly coupled generalized van der Pol–Duffing autogenerators. The essence of the effect revealed is that the synchronized oscillations are not stationary but accompanied by the most intensive e…
[Phys. Rev. E 94, 032223] Published Fri Sep 30, 2016
Axelrod's model with $F=2$ cultural features, where each feature can assume $k$ states drawn from a Poisson distribution of parameter $q$, exhibits a continuous nonequilibrium phase transition in the square lattice. Here we use extensive Monte Carlo simulations and finite size scaling to study the critical behavior of the order parameter $\rho$, which is the fraction of sites that belong to the largest domain of an absorbing configuration averaged over many runs. We find that it vanishes as $\rho \sim \left (q_c^0 - q \right)^\beta$ with $\beta \approx 0.25$ at the critical point $q_c^0 \approx 3.10$ and that the exponent that measures the width of the critical region is $\nu^0 \approx 2.1$. In addition, we find that introduction of long-range links by rewiring the nearest-neighbors links of the square lattice with probability $p$ turns the transition discontinuous, with the critical point $q_c^p$ increasing from $3.1$ to $27.17$, approximately, as $p$ increases from $0$ to $1$. The sharpness of the threshold, as measured by the exponent $\nu^p \approx 1$ for $p>0$, increases with the square root of the number of nodes of the resulting small-world network.
The Google matrix controls the stability of structured ecological and biological networks
Nature Communications, Published online: 30 September 2016; doi:10.1038/ncomms12857
May showed that ecosystem stability decreases above some threshold complexity. Here, Stone generalizes May’s random matrix approach to realistic species interaction networks through a Google-matrix reduction scheme, and provides an explanation for why feasible ecological networks are usually stable.
Author(s): Thomas K. DM. Peron, Jürgen Kurths, Francisco A. Rodrigues, Lutz Schimansky-Geier, and Bernard Sonnenschein
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. With this asymmetric coupling, we analyze patterns in the phase dynamics that coexist with chaotic amplitudes. We specifically inves…[Phys. Rev. E] Published Mon Sep 26, 2016
Author(s): Ghazal Montaseri and Michael Meyer-Hermann
The heterogeneity of coupled oscillators is important for the degree of their synchronization. According to the classical Kuramoto model, larger heterogeneity reduces synchronization. Here, we show that in a model for coupled pancreatic -cells higher diversity of the cells induces higher synchrony. …[Phys. Rev. E] Published Tue Sep 27, 2016
Networks of contacts capable of spreading infectious diseases are often observed to be highly heterogeneous, with the majority of individuals having fewer contacts than the mean, and a significant minority having relatively very many contacts. We derive a two-dimensional diffusion model for the full temporal behavior of the stochastic susceptible-infectious-recovered (SIR) model on such a network, by making use of a time-scale separation in the deterministic limit of the dynamics. This low-dimensional process is an accurate approximation to the full model in the limit of large populations, even for cases when the time-scale separation is not too pronounced, provided the maximum degree is not of the order of the population size.
Many real-world networks exhibit a high degeneracy at few eigenvalues. We show that a simple transformation of the network's adjacency matrix provides an understanding of the origins of occurrence of high multiplicities in the networks spectra. We find that the eigenvectors associated with the degenerate eigenvalues shed light on the structures contributing to the degeneracy. Since these degeneracies are rarely observed in model graphs, we present results for various cancer networks. This approach gives an opportunity to search for structures contributing to degeneracy which might have an important role in a network.
Author(s): Márton Pósfai, Jianxi Gao, Sean P. Cornelius, Albert-László Barabási, and Raissa M. D'Souza
The paradigm of layered networks is used to describe many real-world systems, from biological networks to social organizations and transportation systems. While recently there has been much progress in understanding the general properties of multilayer networks, our understanding of how to control s…
[Phys. Rev. E 94, 032316] Published Mon Sep 26, 2016
Author(s): Yup Kim, Seokjong Park, and Soon-Hyung Yook
We study the mean first passage time (MFPT) of true self-avoiding walks (TSAW's) on various networks as a measure of searching efficiency. From the numerical analysis, we find that the MFPT of TSAW's, \tauTSAW, approaches the theoretical minimum \tauth/N=\frac{1}{2} on synthetic networks whose degre…[Phys. Rev. E] Published Fri Sep 23, 2016
Experiments with networks of discrete reactive bistable electrochemical elements organized in regular and nonregular tree networks are presented to confirm an alternative to the Turing mechanism for the formation of self-organized stationary patterns. The results show that the pattern formation can be described by the identification of domains that can be activated individually or in combinations. The method also enabled the localization of chemical reactions to network substructures and the identification of critical sites whose activation results in complete activation of the system. Although the experiments were performed with a specific nickel electrodissolution system, they reproduced all the salient dynamic behavior of a general network model with a single nonlinearity parameter. Thus, the considered pattern-formation mechanism is very robust, and similar behavior can be expected in other natural or engineered networked systems that exhibit, at least locally, a treelike structure.
Author(s): Hongjie Bi, Xin Hu, S. Boccaletti, Xingang Wang, Yong Zou, Zonghua Liu, and Shuguang Guan
From rhythmic physiological processes to the collective behaviors of technological and natural networks, coherent phases of interacting oscillators are the foundation for the emergence of the system's cooperative functioning. We unveil the existence of a new of such states, occurring in globally cou…[Phys. Rev. Lett.] Published Mon Sep 26, 2016
Author(s): J. Hizanidis, N. Lazarides, and G. P. Tsironis
We report on the emergence of robust multiclustered chimera states in a dissipative-driven system of symmetrically and locally coupled identical superconducting quantum interference device (SQUID) oscillators. The “snakelike” resonance curve of the single SQUID is the key to the formation of the chi…
[Phys. Rev. E 94, 032219] Published Tue Sep 27, 2016
To better design safe and comfortable urban spaces, understanding the nature of human crowd movement is important. However, precise interactions among pedestrians are difficult to measure in the presence of their complex decision-making processes and many related factors. While extensive studies on pedestrian flow through bottlenecks and corridors have been conducted, the dominant mode of interaction in these scenarios may not be relevant in different scenarios. Here, we attempt to decipher the factors that affect human reactions to other individuals from a different perspective. We conducted experiments employing the inflow process in which pedestrians successively enter a confined area (like an elevator) and look for a temporary position. In this process, pedestrians have a wider range of options regarding their motion than in the classical scenarios; therefore, other factors might become relevant. The preference of location is visualized by pedestrian density profiles obtained from recorded pedestrian trajectories. Non-trivial patterns of space acquisition, e.g., an apparent preference for positions near corners, were observed. This indicates the relevance of psychological and anticipative factors beyond the private sphere, which have not been deeply discussed so far in the literature on pedestrian dynamics. From the results, four major factors, which we call flow avoidance, distance cost, angle cost, and boundary preference, were suggested. We confirmed that a description of decision-making based on these factors can give a rise to realistic preference patterns, using a simple mathematical model. Our findings provide new perspectives and a baseline for considering the optimization of design and safety in crowded public areas and public transport carriers.
Author(s): Yogesh S. Virkar, Woodrow L. Shew, Juan G. Restrepo, and Edward Ott
Learning and memory are acquired through long-lasting changes in synapses. In the simplest models, such synaptic potentiation typically leads to runaway excitation, but in reality there must exist processes that robustly preserve overall stability of the neural system dynamics. How is this accomplis…[Phys. Rev. E] Published Mon Sep 26, 2016
The recent availability of geolocalized historical data allows to address quantitatively spatial features of the time evolution of urban areas. Here, we discuss how the number of buildings evolves with population and we show on different datasets (Chicago, $1930-2010$; London, $1900-2015$; New York City, $1790-2013$; Paris, $1861-2011$) that this curve evolves in a 'universal' way with three distinct phases. After an initial pre-urbanization phase, the first phase is a rapid growth of the number of buildings versus population. In a second regime, where residences are converted into offices and stores, the population decreases while the number of buildings stays approximatively constant. In another subsequent -- modern -- phase, the number of buildings and the population grow again and correspond to a re-densification of cities. We propose a simple model based on these simple mechanisms to explain the first two regimes and show that it is in excellent agreement with empirical observations. These results bring evidences for the possibility of constructing a simple model that could serve as a tool for understanding quantitatively urbanization and the future evolution of cities.
Chimera and chimera-like states are characterized in populations of photochemically coupled Belousov–Zhabotinsky (BZ) oscillators. Simple chimeras and chimera states with multiple and traveling phase clusters, phase-slip behavior, and chimera-like states with phase waves are described. Simulations with a realistic model of the discrete BZ system of populations of homogeneous and heterogeneous oscillators are compared with each other and with experimental behavior.
The process of urbanization is one of the most important phenomenon of our societies and it is only recently that the availability of massive amounts of geolocalized historical data allows us to address quantitatively some of its features. Here, we discuss how the number of buildings evolves with population and we show on different datasets (Chicago, $1930-2010$; London, $1900-2015$; New York City, $1790-2013$; Paris, $1861-2011$) that this `fundamental diagram' evolves in a possibly universal way with three distinct phases. After an initial pre-urbanization phase, the first phase is a rapid growth of the number of buildings versus population. In a second regime, where residences are converted into another use (such as offices or stores for example), the population decreases while the number of buildings stays approximatively constant. In another subsequent phase, the number of buildings and the population grow again and correspond to a re-densification of cities. We propose a stochastic model based on these simple mechanisms to reproduce the first two regimes and show that it is in excellent agreement with empirical observations. These results bring evidences for the possibility of constructing a minimal model that could serve as a tool for understanding quantitatively urbanization and the future evolution of cities.