Network Synchronization Process Research Articles

Synchronization processes in fNIRS visibility networks

We employ Kuramoto model to assess the presence of synchronization in individuals who fulfill a cooperation task. Our input data is a couple of signals obtained from functional Near-Infrared Spectroscopy Data Acquisition and Pre-processing technology that is used to capture the brain activity of an individual by measuring the oxyhemoglobin (HbO) level. We consider 1 min signal for individuals in three distinct states: (i) rest; (ii) before a disturb happens; (iii) after the disturbance. We estimate global and local order parameters synchronization with the purpose to compare the conditions of reaching a synchronous state in the networks corresponding to different states for distinct individuals and hemispheres of the prefrontal cortices of same individual. Experimental results confirmed once more that coherent state is reached not for same conditions in both individuals and hemispheres of the prefrontal cortices. Furthermore, condition changes even for different events. The computation of the effective frequencies for each degree class indicates clearly the network difference in rest, before and after disturb. Finally, we investigate the dynamic connectivity matrix and consider the similarity between distinct prefrontal cortices over time.

Neighborhood Selection Synchronization Mechanism-Based Moving Source Localization Using UAV Swarm

To obtain the accurate time difference of arrival (TDOA) and frequency difference of arrival (FDOA) for passive localization in an unmanned aerial vehicle (UAV) swarm, UAV swarm network synchronization is necessary. However, most of the traditional distributed time synchronization protocols are based on iteration, which hinders efficiency improvement. High communication costs and long convergence times are often required in large-scale UAV swarm networks. This paper presents a neighborhood selection-all selection (NS-AS) synchronization mechanism-based moving source localization method for UAV swarms. First, the NS-AS synchronization mechanism is introduced, to model the UAV swarm network synchronization process. Specifically, the UAV neighbors are first grouped by sector, and the most representative neighbors are selected from each sector for the state update calculation. When the UAV swarm network reaches a fully connected state, the synchronization mechanism is switched to select all neighbors, to improve the convergence speed. Then, the TDOA-FDOA joint localization algorithm is employed to locate the moving radiation source. Through simulation, the effectiveness of the proposed method is verified by the system convergence and localization performance under different parameters. Experimental results show that the synchronization mechanism based on NS-AS effectively improves the convergence speed of the system while ensuring the accuracy of moving radiation source localization.

Searching for Best Network Topologies with Optimal Synchronizability: A Brief Review

The Laplacian eigenvalue spectrum of a complex network contains a great deal of information about the network topology and dynamics, particularly affecting the network synchronization process and performance. This article briefly reviews the recent progress in the studies of network synchronizability, regarding its spectral criteria and topological optimization, and explores the role of higher-order topologies in measuring the optimal synchronizability of large-scale complex networks.

Network synchronization, stability and rhythmic processes in a diffusive mean-field coupled SEIR model

Connectivity and rates of movement have profound effect on the persistence and extinction of infectious diseases. The emerging disease spread rapidly, due to the movement of infectious persons to some other regions, which has been witnessed in case of novel coronavirus disease 2019 (COVID-19). So, the networks and the epidemiology of directly transmitted infectious diseases are fundamentally linked. Motivated by the recent empirical evidence on the dispersal of infected individuals among the patches, we present the epidemic model SEIR (Susceptible-Exposed-Infected-Recovered) in which the population is divided into patches which form a network and the patches are connected through mean-field diffusive coupling. The corresponding unstable epidemiology classes will be synchronized and achieve stable state when the patches are coupled. Apart from synchronization and stability, the coupled model enables a range of rhythmic processes such as birhythmicity and rhythmogenesis which have not been investigated in epidemiology. The stability of Disease Free Equilibrium (or Endemic Equilibrium) is attained through cessation of oscillation mechanism namely Oscillation Death (OD) and Amplitude Death (AD). Corresponding to identical and non-identical epidemiology classes of patches, the different steady states are obtained and its transition is taking place through Hopf and transcritical bifurcation.

Generic Mechanism for Waveform Regulation and Synchronization of Oscillators: An Application for Robot Behavior Diversity Generation.

While nonlinear oscillators have been widely used for central pattern generators to produce basic rhythmic signals for robot locomotion control, methods to shape and regulate the signal waveform without changing the characteristics of the oscillators have not been fully investigated, especially during the network synchronization process. To illustrate the principle and process of waveform regulation of nonlinear oscillators in detail and ensure that the influence can be controlled, we present a method for waveform regulation and synchronization and analyze the relationship of different factors (e.g., initial conditions, network parameters, phase, and waveform regulation factors) in synchronization deviation. Then, the method is indicated to be effective in other commonly used nonlinear oscillators and neural oscillators. As an example application, a three-layer behavioral control architecture for a legged robot is constructed based on the proposed method. Modules for the body behavior, leg coordination, and single-leg adjustment are established to realize diverse robot behaviors. The effectiveness of the method is validated by a series of experiments. The results prove that the method performs well in terms of signal control accuracy, behavior pattern diversity, and smooth motion transition.

Exponential synchronization of uncertain networks with the switching topology based on sliding mode technology

We investigate the exponential synchronization of uncertain networks with the switching topology based on sliding mode technology. In this work, the network controller and the adaptive law of uncertain parameter are designed to ensure the exponential synchronization between uncertain networks with the switching topology and the synchronization target. In addition, the synchronization technology is suitable for any topology network, and in the network synchronization process, the switching of the network topology is not restricted, that is, it can be switched at any time according to the actual requirement. At last, the effects of the exponential synchronization criteria are verified through the numerical example.

Desynchronization by phase slip patterns in networks of pulse-coupled oscillators with delays

Coupling delays may cause drastic changes in the dynamics of oscillatory networks. In the present paper we investigate how coupling delays alter synchronization processes in networks of all-to-all coupled pulse oscillators. We derive an analytic criterion for the stability of synchrony and study the synchronization areas in the space of the delay and coupling strength. Specific attention is paid to the scenario of destabilization on the borders of the synchronization area. We show that in bifurcation points the system possesses homoclinic loops, which give rise to complex long- or quasi-periodic solutions. These newly born solutions are characterized by a synchronous group, from which an oscillator periodically escapes, laps one period, and rejoins. We call such a dynamical regime “phase slip patterns”.

Relationship of Topology, Multiscale Phase Synchronization, and State Transitions in Human Brain Networks.

How the brain reconstitutes consciousness and cognition after a major perturbation like general anesthesia is an important question with significant neuroscientific and clinical implications. Recent empirical studies in animals and humans suggest that the recovery of consciousness after anesthesia is not random but ordered. Emergence patterns have been classified as progressive and abrupt transitions from anesthesia to consciousness, with associated differences in duration and electroencephalogram (EEG) properties. We hypothesized that the progressive and abrupt emergence patterns from the unconscious state are associated with, respectively, continuous and discontinuous synchronization transitions in functional brain networks. The discontinuous transition is explainable with the concept of explosive synchronization, which has been studied almost exclusively in network science. We used the Kuramato model, a simple oscillatory network model, to simulate progressive and abrupt transitions in anatomical human brain networks acquired from diffusion tensor imaging (DTI) of 82 brain regions. To facilitate explosive synchronization, distinct frequencies for hub nodes with a large frequency disassortativity (i.e., higher frequency nodes linking with lower frequency nodes, or vice versa) were applied to the brain network. In this simulation study, we demonstrated that both progressive and abrupt transitions follow distinct synchronization processes at the individual node, cluster, and global network levels. The characteristic synchronization patterns of brain regions that are “progressive and earlier” or “abrupt but delayed” account for previously reported behavioral responses of gradual and abrupt emergence from the unconscious state. The characteristic network synchronization processes observed at different scales provide new insights into how regional brain functions are reconstituted during progressive and abrupt emergence from the unconscious state. This theoretical approach also offers a principled explanation of how the brain reconstitutes consciousness and cognitive functions after physiologic (sleep), pharmacologic (anesthesia), and pathologic (coma) perturbations.

Vulnerability of Network Synchronization Processes: A Minimum Energy Perspective

We study the vulnerability of a linear network synchronization process to intrusion at a single network component, from a graph-theoretic perspective. Specifically, we model the intruder as seeking to move the state of the synchronization process to an undesirable value or set via a local actuation. We measure the network vulnerability in terms of the minimum or expected minimum actuation energy required of the adversary to achieve the goal, which is related to the inverse of the controllability Gramian for the process and statistics defined thereof (e.g., its trace and determinant). Using explicit formulas for the Gramian inverse and its associated statistics together with algebraic graph-theory concepts, we then develop structural and graph-theoretic characterizations of the energy-based vulnerability measures.

Detecting link failures in complex network processes using remote monitoring

We study whether local structural changes in a complex network can be distinguished from passive remote time-course measurements of the network’s dynamics. Specifically the detection of link failures in a network synchronization process from noisy measurements at a single network component is considered. By phrasing the detection task as a Maximum A Posteriori Probability hypothesis testing problem, we are able to obtain conditions under which the detection is (1) improved over the a priori and (2) asymptotically perfect, in terms of the network spectrum and graph. We find that, in the case where the detector has knowledge of the network’s state, perfect detection is possible under general connectivity conditions regardless of the measurement location. When the detector does not have state knowledge, a remote signature permits improved but not perfect detection, under the same connectivity conditions. At its essence, detectability is achieved because of the close connection between a network’s topology, its eigenvalues and local response characteristics.

Oscillatory neural networks based on the Kuramoto model for cluster analysis

This paper presents the results of a study of synchronization processes in oscillatory neural networks of various structures based on the Kuramoto model. The estimates of synchronization processes occurring in the oscillatory networks are examined. The results of studying the practical application of oscillatory networks for solving cluster analysis problems are presented.

Synchronization processes in clustered networks with different inter-cluster couplings

This paper studies the synchronizability and the synchronization processes of three kinds of clustered networks with different inter-cluster couplings, where each clustered network is composed of two BA scale-free subnets. The clustered network is called a TWD network if the inter-cluster coupling is a two-way coupling, but it is called a BDS network if the small subnet is driven by the big one, and is called an SDB network if the big subnet is driven by the small one. The result shows that when the ratio of node number of small subnet to that of big one is larger than a critical value, the whole synchronizability of the TWD networks is better than that of the BDS networks; however, when this ratio is smaller than the critical value, the whole synchronizability of the TWD networks is weaker than that of the BDS ones, the whole synchronizability of the SDB networks is always the worst. For a one-way-driven clustered network, the synchronizability is just related to the node number of the driven subnet and the number of the inter-links, but has nothing to do with the node number of the driving subnet. The increase in the inter-links can reduce the synchronous speed of the subnet at the beginning but may enhance the synchronizability of the whole network eventually. The Kuramoto phase oscillators are taken as the network nodes to further study the synchronization process of the three-clustered networks for different cases, and the correctness of the above conclusions are evidenced.

Initial-Condition Estimation in Network Synchronization Processes: Algebraic and Graphical Characterizations of the Estimator

We pursue a graph-theoretic analysis of state inference in network synchronization (or diffusive) processes. Precisely, we study estimation of a non-random initial condition of a canonical synchronization dynamics defined on a graph, from noisy observations at a single network node. By characterizing the maximum-likelihood estimation of the initial condition and the associated Cramer-Rao bound, we identify graph properties (e.g., symmetries, interconnection strengths, spectral measures) that determine 1) whether or not estimation is possible and 2) the quality of the estimate.

Segment Tracking via a Spatiotemporal Linking Process including Feedback Stabilization in an n-D Lattice Model

Model-free tracking is important for solving tasks such as moving-object tracking and action recognition in cases where no prior object knowledge is available. For this purpose, we extend the concept of spatially synchronous dynamics in spin-lattice models to the spatiotemporal domain to track segments within an image sequence. The method is related to synchronization processes in neural networks and based on superparamagnetic clustering of data. Spin interactions result in the formation of clusters of correlated spins, providing an automatic labeling of corresponding image regions. The algorithm obeys detailed balance. This is an important property as it allows for consistent spin-transfer across subsequent frames, which can be used for segment tracking. Therefore, in the tracking process the correct equilibrium will always be found, which is an important advance as compared with other more heuristic tracking procedures. In the case of long image sequences, i.e., movies, the algorithm is augmented with a feedback mechanism, further stabilizing segment tracking.

Biologically Inspired Intercellular Slot Synchronization

The present article develops a decentralized interbase station slot synchronization algorithm suitable for cellular mobile communication systems. The proposed cellular firefly synchronization (CelFSync) algorithm is derived from the theory of pulse-coupled oscillators, common to describe synchronization phenomena in biological systems, such as the spontaneous synchronization of fireflies. In order to maintain synchronization among base stations (BSs), even when there is no direct link between adjacent BSs, some selected user terminals (UTs) participate in the network synchronization process. Synchronization emerges by exchanging two distinct synchronization words, one transmitted by BSs and the other by active UTs, without any a priori assumption on the initial timing misalignments of BSs and UTs. In large-scale networks with inter-BS site distances up to a few kilometers, propagation delays severely affect the attainable timing accuracy of CelFSync. We show that by an appropriate combination of CelFSync with the timing advance procedure, which aligns uplink transmission of UTs to arrive simultaneously at the BS, a timing accuracy within a fraction of the inter-BS propagation delay is retained.

Synchronization in networks of spatially extended systems

Synchronization processes in networks of spatially extended dynamical systems are analytically and numerically studied. We focus on the relevant case of networks whose elements (or nodes) are spatially extended dynamical systems, with the nodes being connected with each other by scalar signals. The stability of the synchronous spatio-temporal state for a generic network is analytically assessed by means of an extension of the master stability function approach. We find an excellent agreement between the theoretical predictions and the data obtained by means of numerical calculations. The efficiency and reliability of this method is illustrated numerically with networks of beam-plasma chaotic systems (Pierce diodes). We discuss also how the revealed regularities are expected to take place in other relevant physical and biological circumstances.

SYNCHRONIZATION IN NETWORKS OF SLIGHTLY NONIDENTICAL ELEMENTS

We study synchronization processes in networks of slightly nonidentical chaotic systems, for which a complete invariant synchronization manifold does not rigorously exist. We show and quantify how a slightly dispersed distribution in parameters can be properly modeled by a noise term affecting the stability of the synchronous invariant solution emerging for identical systems when the parameter is set at the mean value of the original distribution.

Synchronization processes in complex networks

During the last decades the emergence of collective dynamics in large networks of coupled units has been investigated in fields such as optics, chemistry, biology and ecology. Recently, complex networks have provided a challenging framework for the study of synchronization of dynamical units, based on the interplay between complexity in the overall topology and local dynamical properties of the coupled units. In this work, we review the constructive role played by such complex wirings for the synchronization of networks of coupled dynamical systems. We review the main techniques that have been proposed for assessing the propensity for synchronization (synchronizability) of a given networked system. We will also describe the main applications, especially in the view of selecting the optimal topology in the coupling configuration that provides enhancement of the synchronization features.

Synchronization processes in complex networks

We present an extended analysis, based on the dynamics towards synchronization of a system of coupled oscillators, of the hierarchy of communities in complex networks. In the synchronization process, different structures corresponding to well defined communities of nodes appear in a hierarchical way. The analysis also provides a useful connection between synchronization dynamics, complex networks topology and spectral graph analysis.

Synchronization and desynchronization of complex dynamical networks: an engineering viewpoint

We study synchronization and desynchronization of a complex network of chaotic dynamical systems, in both continuous-time and discrete-time cases. With proved synchronization conditions, we illustrate network synchronization and desynchronization processes by a prototype composing of Henon maps in a scale-free network. We show that synchronization and desynchronization of such a complex dynamical network can be determined by the network topology and the maximum Lyapunov exponent of the individual chaotic nodes.