Spectral universality of phase synchronization in non-identical oscillator networks

We employ a spectral decomposition method to analyze synchronization of a non-identical oscillator network. We study the case that a small parameter mismatch of oscillators is characterized by one parameter and phase synchronization is observed. We derive a linearized equation for each eigenmode of the coupling matrix. The parameter mismatch is reflected on inhomogeneous term in the linearized equation. We find that the oscillation of each mode is essentially characterized only by the eigenvalue of the coupling matrix with a suitable normalization. We refer to this property as spectral universality, because it is observed irrespective of network topology. Numerical results in various network topologies show good agreement with those based on linearized equation. This universality is also observed in a system driven by additive independent Gaussian noise.     

Consensus on de Bruijn graphs

We study the consensus dynamics with or without time-delays on directed and undirected de Bruijn graphs. Our results show that consensus on an undirected de Bruijn graph has a lower converging speed and larger time-delay tolerance in comparison with that on an undirected scale-free network. Although there is not much difference between the eigenvalue ratios of the two undirected networks, we found that their dynamical properties are remarkably different; consequently, it is seemingly more informative to consider the second smallest and the largest eigenvalues separately rather than considering their ratio in the study of synchronization of a coupled oscillators network. Moreover, our study on directed de Bruijn graphs reveals that properly setting directions on edges can improve the converging speed and time-delay tolerance simultaneously.     

Analytical treatment of synchronization of spin-torque oscillators by microwave magnetic fields

An analytical approach is presented for the study of synchronization effects in spin-transfer-driven nanomagnets subjected to radio-frequency magnetic fields. The conditions are derived and discussed under which the current-induced magnetization precession is synchronized by the radio-frequency field. Exact analytical results are obtained for the case when the problem exhibits uniaxial symmetry around the axis perpendicular to the device plane. It is demonstrated that the magnetization dynamics under nonzero current and nonzero rf field is identical in structure to that under zero current. On this basis, analytical predictions are obtained for: the existence of phase-locking between current-induced magnetization precession and rf field oscillations; the frequency pulling effect in proximity of phase locking; the occurrence of hysteresis effects in phase-locking as a function of the spin-polarized current. The proposed approach is valid for arbitrary rf field amplitude and current intensity.     

Enhancing synchronizability by weight randomization on regular networks

In weighted networks, redistribution of link weights can effectively change the properties of networks, even though the corresponding binary topology remains unchanged. In this paper, the effects of weight randomization on synchronization of coupled chaotic maps is investigated on regular weighted networks. The results reveal that synchronizability is enhanced by redistributing of link weights, i.e. coupled maps reach complete synchronization with lower cost. Furthermore, we show numerically that the heterogeneity of link weights could improve the complete synchronization on regular weighted networks.     

Epidemic threshold and phase transition in scale-free networks with asymmetric infection

We study the SIS epidemic dynamics on scale-freeweighted networks with asymmetric infection, by both analysis andnumerical simulations, with focus on the epidemic threshold aswell as critical behaviors. It is demonstrated that the asymmetryof infection plays an important role: we could redistribute theasymmetry to balance the degree heterogeneity of the network andthen to restore the epidemic threshold to a fnite value. On theother hand, we show that the absence of the epidemic threshold isnot so bad as commented previously since the prevalence grows veryslowly in this case and one could only protect a few vertices toprevent the diseases propagation.     

Rank-based model for weighted network with hierarchical organization and disassortative mixing

In this paper, we study a rank-based model for weighted network. The evolution rule of the network is based on the ranking of node strength, which couples the topological growth and the weight dynamics. Analytically and by simulations, we demonstrate that the generated networks recover the scale-free distributions of degree and strength in the whole region of the growth dynamics parameter (α>0). Moreover, this network evolution mechanism can also produce scale-free property of weight, which adds deeper comprehension of the networks growth in the presence of incomplete information. We also characterize the clustering and correlation properties of this class of networks. It is showed that at α=1 a structural phase transition occurs, and for α>1 the generated network simultaneously exhibits hierarchical organization and disassortative degree correlation, which is consistent with a wide range of biological networks.     

On the rich-club effect in dense and weighted networks

For many complex networks present in nature only a single instance, usually of large size, is available. Any measurement made on this single instance cannot be repeated on different realizations. In order to detect significant patterns in a real-world network it is therefore crucial to compare the measured results with a null model counterpart. Here we focus on dense and weighted networks, proposing a suitable null model and studying the behaviour of the degree correlations as measured by the rich-club coefficient. Our method solves an existing problem with the randomization of dense unweighted graphs, and at the same time represents a generalization of the rich-club coefficient to weighted networks which is complementary to other recently proposed ones.     

Synchronization of multi-phase oscillators: an Axelrod-inspired model

Inspired by Axelrod’s model of culture dissemination, we introduce and analyze a model for a population of coupled oscillators where different levels of synchronization can be assimilated to different degrees of cultural organization. The state of each oscillator is represented by a set of phases, and the interaction – which occurs between homologous phases – is weighted by a decreasing function of the distance between individual states. Both ordered arrays and random networks are considered. We find that the transition between synchronization and incoherent behaviour is mediated by a clustering regime with rich organizational structure, where any two oscillators can be synchronized in some of their phases, while their remain unsynchronized in the others.     

Topological properties of phylogenetic trees in evolutionary models

The extent to which evolutionary processes affect the shape of phylogenetic trees is an important open question. Analyses of small trees seem to detect non-trivial asymmetries which are usually ascribed to the presence of correlations in speciation rates. Many models used to construct phylogenetic trees have an algorithmic nature and are rarely biologically grounded. In this article, we analyze the topological properties of phylogenetic trees generated by different evolutionary models (populations of RNA sequences and a simple model with inheritance and mutation) and compare them with the trees produced by known uncorrelated models as the backward coalescent, paying special attention to large trees. Our results demonstrate that evolutionary parameters as mutation rate or selection pressure have a weak influence on the scaling behavior of the trees, while the size of phylogenies strongly affects measured scaling exponents. Within statistical errors, the topological properties of phylogenies generated by evolutionary models are compatible with those measured in balanced, uncorrelated trees.     

Interplay of noise and coupling in heterogeneous ensembles of phase oscillators

We study the effects of noise on the collective dynamics of an ensemble of coupled phase oscillators whose natural frequencies are all identical, but whose coupling strengths are not the same all over the ensemble. The intensity of noise can also be heterogeneous, representing diversity in the individual responses to external fluctuations. We show that the desynchronization transition induced by noise may be completely suppressed, even for arbitrarily large noise intensities, is the distribution of coupling strengths decays slowly enough for large couplings. Equivalently, if the response to noise of a sufficiently large fraction of the ensemble is weak enough, desynchronization cannot occur. The two effects combine with each other when the response to noise and the coupling strength of each oscillator are correlated. This combination is quantitatively characterized and illustrated with explicit examples.     

Better synchronizability predicted by a new coupling method

In this paper, inspired by the idea that different nodes should play different roles in network synchronization, we bring forward a coupling method where the coupling strength of each node depends on its neighbors' degrees. Compared with the uniform coupled method and the recently proposed Motter-Zhou-Kurths method, the synchronizability of scale-free networks can be remarkably enhanced by using the present coupling method, and the highest network synchronizability is achieved at β=1 which is similar to a method introduced in [AIP Conf. Proc. 776, 201 (2005)].     

Global firing induced by network disorder in ensembles of active rotators

We study the influence of repulsive interactions on an ensemble of coupled excitable rotators. We find that a moderate fraction of repulsive interactions can trigger global firing of the ensemble. The regime of global firing, however, is suppressed in sufficiently large systems if the network of repulsive interactions is fully random, due to self-averaging in its degree distribution. We thus introduce a model of partially random networks with a broad degree distribution, where self-averaging due to size growth is absent. In this case, the regime of global firing persists for large sizes. Our results extend previous work on the constructive effects of diversity in the collective dynamics of complex systems.     

Multivariate analysis of spatially heterogeneous phase synchronisation in complex systems: application to self-organised control of material flows in networks

Networks of interacting components are a class of complex systems that has attracted considerable interest over the last decades. In particular, if the dynamics of the autonomous components is characterised by an oscillatory behaviour, different types of synchronisation can be observed in dependence on the type and strength of interactions. In this contribution, we study the transition from non-synchronised to synchronised phase dynamics in complex networks. The most common approach to quantify the degree of phase synchronisation in such systems is the consideration of measures of phase coherence which are averaged over all pairs of interacting components. However, this approach implicitly assumes a spatially homogeneous synchronisation process, which is typically not present in complex networks. As a potential alternative, two novel methods of multivariate phase synchronisation analysis are considered: synchronisation cluster analysis (SCA) and the linear variance decay (LVD) dimension method. The strengths and weaknesses of the traditional as well as both new approaches are briefly illustrated for a Kuramoto model with long-range coupling. As a practical application, we study how spatial heterogeneity influences the transition to phase synchronisation in traffic networks where intersecting material flows are subjected to a self-organised decentralised control. We find that the network performance and the degree of phase synchronisation are closely related to each other and decrease significantly in the case of structural heterogeneities. The influences of the different parameters of our control approach on the synchronisation process are systematically studied, yielding a sequence of Arnold tongues which correspond to different locking modes.     

Heterogeneous network with distance dependent connectivity

We investigate a network model based on an infinite regular square lattice embedded in the Euclidean plane where the node connection probability is given by the geometrical distance of nodes. We show that the degree distribution in the basic model is sharply peaked around its mean value. Since the model was originally developed to mimic the social network of acquaintances, to broaden the degree distribution we propose its generalization. We show that when heterogeneity is introduced to the model, it is possible to obtain fat tails of the degree distribution. Meanwhile, the small-world phenomenon present in the basic model is not affected. To support our claims, both analytical and numerical results are obtained.     

Response of boolean networks to perturbations

We evaluate the probability that a Boolean network returns to an attractor after perturbing h nodes. We find that the return probability as function of h can display a variety of different behaviours, which yields insights into the state-space structure. In addition to performing computer simulations, we derive analytical results for several types of Boolean networks, in particular for Random Boolean Networks. We also apply our method to networks that have been evolved for robustness to small perturbations, and to a biological example.     

Efficiency based strategy spreading in the prisoner’s dilemma game

In contrast to well-mixed populations, discrete interaction patterns have been shown to support cooperation in the prisoner’s dilemma game, and a scale-free network topology may even lead to a dominance of cooperation over defection. The majority of studies assumes a strategy adoption scheme based on accumulated payoffs. The use of accumulated payoffs, however, is incompatible with the integral property of the underlying replicator dynamics to be invariant under a positive affine transformation of the payoff function. We show that using instead the payoff per interaction to determine the strategy spread, which has been suggested recently and recovers the required invariance, results in fundamentally different dynamical behavior under a synchronized strategy adoption considered here. Most notably, in such an efficiency based scenario the advantage of a scale-free network topology vanishes almost completely. We present a detailed explanation of the fundamentally altered dynamical behavior.     

Chaos synchronization in networks of coupled maps with time-varying topologies

Complexity of dynamical networks can arise not only from the complexity of the topological structure but also from the time evolution of the topology. In this paper, we study the synchronous motion of coupled maps in time-varying complex networks both analytically and numerically. The temporal variation is rather general and formalized as being driven by a metric dynamical system. Four network models are discussed in detail in which the interconnections between vertices vary through time randomly. These models are: 1) i.i.d. sequences of random graphs with fixed wiring probability, 2) groups of graphs with random switches between the individual graphs, 3) graphs with temporary random failures of nodes, and 4) the meet-for-dinner model where the vertices are randomly grouped. We show that the temporal variation and randomness of the connection topology can enhance synchronizability in many cases; however, there are also instances where they reduce synchronizability. In analytical terms, the Hajnal diameter of the coupling matrix sequence is presented as a measure for the synchronizability of the graph topology. In topological terms, the decisive criterion for synchronization of coupled chaotic maps is that the union of the time-varying graphs contains a spanning tree.     

Incompatibility networks as models of scale-free small-world graphs

We make a mapping from Sierpinski fractals to a new class of networks, the incompatibility networks, which are scale-free, small-world, disassortative, and maximal planar graphs. Some relevant characteristics of the networks such as degree distribution, clustering coefficient, average path length, and degree correlations are computed analytically and found to be peculiarly rich. The method of network representation can be applied to some real-life systems making it possible to study the complexity of real networked systems within the framework of complex network theory.     

Firing activity of complex space-clamped FitzHugh-Nagumo neural networks

We investigate how firing activity of complex neural networks depends on the random long-range connections and coupling strength. Network elements are described by excitable space-clamped FitzHugh-Nagumo (SCFHN) neurons with the values of parameters at which no firing activity occurs. It is found that for a given appropriate coupling strength C, there exists a critical fraction of random connections (or randomness) p^*, such that if p > p^* the firing neurons, which are absent in the nearest-neighbor network, occur. The firing activity becomes more frequent as randomness p is further increased. On the other hand, when the p is smaller, there are no active neurons in network, no matter what the value of C is. For a given larger p, there exist optimal coupling strength levels, where firing activity reaches its maximum. To the best of our knowledge, this is a novel mechanism for the emergence of firing activity in neurons.     

Fast algorithms for ring recognition and electron identification in the CBM RICH detector

The algorithm for recognition of Cherenkov radiation rings based on the Hough Transform Method (HTM), as well as the innovations which allow one to considerably speed up the HTM algorithm, are described. An ellipse-fitting algorithm has been elaborated, because most of the CBM RICH rings have elliptic shapes; moreover, it helps improve the ring-track matching and electron identification procedures. An elaborated procedure of the radius correction is also presented. A detailed study of the procedure of fake ring elimination by artificial neural networks is given. The results of the primary electron identification are presented. All developed algorithms were tested on large statistics of simulated events and are included into the CBM software framework for common use.