Shuguang Guan

Explosive Synchronization in Adaptive and Multilayer Networks

At this time, explosive synchronization (ES) of networked oscillators is thought of as being rooted in the setting of specific microscopic correlation features between the natural frequencies of the oscillators and their effective coupling strengths. We show that ES is, in fact, far more general and can occur in adaptive and multilayer networks in the absence of such correlation properties. We first report evidence of ES for single-layer networks where a fraction f of the nodes have links adaptively controlled by a local order parameter, and we then extend the study to a variety of two-layer networks with a fraction f of their nodes coupled with each other by means of dependency links. In the latter case, we give evidence of ES regardless of the differences in the frequency distribution, in the topology of connections between the layers, or both. Finally, we provide a rigorous, analytical treatment to properly ground all of the observed scenarios and to advance the understanding of the actual mechanisms at the basis of ES in real-world systems.

Explosive transitions in complex networks’ structure and dynamics: Percolation and synchronization

Abstract Percolation and synchronization are two phase transitions that have been extensively studied since already long ago. A classic result is that, in the vast majority of cases, these transitions are of the second-order type, i.e. continuous and reversible. Recently, however, explosive phenomena have been reported in complex networks’ structure and dynamics, which rather remind first-order (discontinuous and irreversible) transitions. Explosive percolation, which was discovered in 2009, corresponds to an abrupt change in the network’s structure, and explosive synchronization (which is concerned, instead, with the abrupt emergence of a collective state in the networks’ dynamics) was studied as early as the first models of globally coupled phase oscillators were taken into consideration. The two phenomena have stimulated investigations and debates, attracting attention in many relevant fields. So far, various substantial contributions and progresses (including experimental verifications) have been made, which have provided insights on what structural and dynamical properties are needed for inducing such abrupt transformations, as well as have greatly enhanced our understanding of phase transitions in networked systems. Our intention is to offer here a monographic review on the main-stream literature, with the twofold aim of summarizing the existing results and pointing out possible directions for future research.

Exact solution for first-order synchronization transition in a generalized Kuramoto model

First-order, or discontinuous, synchronization transition, i.e. an abrupt and irreversible phase transition with hysteresis to the synchronized state of coupled oscillators, has attracted much attention along the past years. We here report the analytical solution of a generalized Kuramoto model, and derive a series of exact results for the first-order synchronization transition, including i) the exact, generic, solutions for the critical coupling strengths for both the forward and backward transitions, ii) the closed form of the forward transition point and the linear stability analysis for the incoherent state (for a Lorentzian frequency distribution), and iii) the closed forms for both the stable and unstable coherent states (and their stabilities) for the backward transition. Our results, together with elucidating the first-order nature of the transition, provide insights on the mechanisms at the basis of such a synchronization phenomenon.

Fourier-Bessel analysis of patterns in a circular domain

This paper explores the use of the Fourier–Bessel analysis for characterizing patterns in a circular domain. A set of stable patterns is found to be well-characterized by the Fourier–Bessel functions. Most patterns are dominated by a principal Fourier–Bessel mode [n, m] which has the largest Fourier–Bessel decomposition amplitude when the control parameter R is close to a corresponding non-trivial root (ρn,m) of the Bessel function. Moreover, when the control parameter is chosen to be close to two or more roots of the Bessel function, the corresponding principal Fourier–Bessel modes compete to dominate the morphology of the patterns.

The development of generalized synchronization on complex networks

In this paper, we numerically investigate the development of generalized synchronization (GS) on typical complex networks, such as scale-free networks, small-world networks, random networks, and modular networks. By adopting the auxiliary-system approach to networks, we observe that GS generally takes place in oscillator networks with both heterogeneous and homogeneous degree distributions, regardless of whether the coupled chaotic oscillators are identical or nonidentical. We show that several factors, such as the network topology, the local dynamics, and the specific coupling strategies, can affect the development of GS on complex networks.

A coevolving model based on preferential triadic closure for social media networks.

The dynamical origin of complex networks, i.e., the underlying principles governing network evolution, is a crucial issue in network study. In this paper, by carrying out analysis to the temporal data of Flickr and Epinions–two typical social media networks, we found that the dynamical pattern in neighborhood, especially the formation of triadic links, plays a dominant role in the evolution of networks. We thus proposed a coevolving dynamical model for such networks, in which the evolution is only driven by the local dynamics–the preferential triadic closure. Numerical experiments verified that the model can reproduce global properties which are qualitatively consistent with the empirical observations.

A wavelet method for the characterization of spatiotemporal patterns

This paper introduces a wavelet-based method for the characterization of spatiotemporal patterns. Based on the wavelet multiresolution analysis, two wavelet indices, multiscale accumulative density (MAD) and multiscale accumulative change (MAC), are proposed for the characterization of the dynamics of the spatiotemporal patterns. Both indices are constructed by using orthogonal wavelet projection operators. The MAD is a measure of the spatial complexity of a pattern at a given time, whereas the MAC characterizes the spatial complexity of instantaneous change of the spatiotemporal patterns at a given time. The ratio of the MAD indices between the lowest and the highest scales reflects the order of coherence in a pattern. The time series of both MAD and MAC provide the dynamical information of morphological pattern evolutions. Numerical experiments based on the Cahn–Hilliard equation indicate that the proposed method is efficient for quantitatively characterizing the dynamics of the spatiotemporal patterns.

Coexistence of Quantized, Time Dependent, Clusters in Globally Coupled Oscillators.

Hongjie Bi,1, ∗ Xin Hu,2, ∗ S. Boccaletti,3, 4, † Xingang Wang,5 Yong Zou,1 Zonghua Liu,1 and Shuguang Guan1, ‡ Department of Physics, East China Normal University, Shanghai 200241, China Key Lab of Nanodevices and Applications-CAS & Collaborative Innovation Center of Suzhou Nano Science and Technology, Suzhou Institute of Nano-Tech and Nano-Bionics, Chinese Academy of Sciences, Suzhou 215123, China. CNR-Institute of Complex Systems, Via Madonna del Piano, 10, 50019 Sesto Fiorentino, Florence, Italy The Embassy of Italy in Tel Aviv, 25 Hamered street, 68125 Tel Aviv, Israel School of Physics and Information Technology, Shaanxi Normal University, Xian 710062, China

Protecting infrastructure networks from cost-based attacks

It is well known that heterogeneous networks are vulnerable to the intentional removal of a small fraction of highly connected or loaded nodes, implying that to protect the network effectively, the important nodes should be allocated more defense resource than the others. However, if too much resource is allocated to the few important nodes, the numerous less-important nodes will be less protected, which if attacked together can still lead to devastating damage. A natural question is therefore how to efficiently distribute the limited defense resource among the network nodes such that the network damage is minimized against any attack strategy. In this paper, taking into account the factor of attack cost, the problem of network security is reconsidered in terms of efficient network defense against cost-based attacks. The results show that, for a general complex network, there exists an optimal distribution of the defense resource with which the network is best protected from cost-based attacks. Furthermore, it is found that the configuration of the optimal defense is dependent on the network parameters. Specifically, networks of larger size, sparser connection and more heterogeneous structure will more likely benefit from the defense optimization.

Desynchronization and on-off intermittency in complex networks

Most existing works on synchronization in complex networks concern the synchronizability and its dependence on network topology. While there has also been work on desynchronization wave patterns in networks that are regular or nearly regular, little is known about the dynamics of synchronous patterns in complex networks. We find that, when a complex network becomes desynchronized, a giant cluster of a vast majority of synchronous nodes can form. A striking phenomenon is that the size of the giant cluster can exhibit an extreme type of intermittent behavior: on-off intermittency. We articulate a physical theory to explain this behavior. This phenomenon may have implications to the evolution of real-world systems.