Synchronization in complex networks

Abstract

Synchronization processes in populations of locally interacting elements are in the focus of intense research in physical, biological, chemical, technological and social systems. The many efforts devoted to understand synchronization phenomena in natural systems take now advantage of the recent theory of complex networks. In this review, we report the advances in the comprehension of synchronization phenomena when oscillating elements are constrained to interact in a complex network topology. We also overview the new emergent features coming out from the interplay between the structure and the function of the underlying pattern of connections. Extensive numerical work as well as analytical approaches to the problem are presented. Finally, we review several applications of synchronization in complex networks to different disciplines: biological systems and neuroscience, engineering and computer science, and economy and social sciences.

Final version published in Physics Reports. More information available at http://synchronets.googlepages.com/

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• Network desynchronization by non-Gaussian fluctuations
• Adaptive frequency-based modeling of whole-brain oscillations: Predicting regional vulnerability and hazardousness rates
• Network synchronization with periodic coupling
• Motion-induced synchronization in metapopulations of mobile agents
• Ginzburg-Landau approximation for self-sustained oscillators weakly coupled on complex directed graphs
• Prevalence and scalable control of localized networks
• Eigenvector-based analysis of cluster synchronization in general complex networks of coupled chaotic oscillators
• Directed Flow of Information in Chimera States
• The dynamics of laser droplet generation
• Impact of network structure on a model of diffusion and competitive interaction
• Network Alignment
• Modular structure in C. elegans neural network and its response to external localized stimuli
• Self-organized explosive synchronization in complex networks: Emergence of synchronization bombs
• Structural and functional networks in complex systems with delay
• Gaussian noise and the two-network frustrated Kuramoto model
• Optimal phase synchronization in networks of phase-coherent chaotic oscillators
• Defects Superdiffusion and Unbinding in a 2D XY Model of Self-Driven Rotors
• Synchronization of nearly-identical dynamical systems. I Size instability
• Global phase synchronization in an array of time-delay systems
• Synchronization in repulsively coupled oscillators
• On the onset of synchronization of Kuramoto oscillators in scale-free networks
• Synchronization of Reinforced Stochastic Processes with a Network-based Interaction
• Effective Bounds on Network-Size for Anti-phase Synchronization
• Benjamin-Feir instabilities on directed networks
• Topologically Protected Loop Flows in High Voltage AC Power Grids
• Clusters in nonsmooth oscillator networks
• Lower bound of assortativity coefficient in scale-free networks
• Random walks with long-range steps generated by functions of Laplacian matrices
• Nonlinear preferential rewiring in fixed-size networks as a diffusion process
• Inverse synchronizations in coupled time-delay systems with inhibitory coupling
• Synchronization transition in Sakaguchi-Kuramoto model on complex networks with partial degree-frequency correlation
• Stability and chaos in coupled two-dimensional maps on Gene Regulatory Network of bacterium E.Coli
• Synchronization Probability in Large Random Networks
• The thermodynamic efficiency of the Lorenz system
• Conedy: a scientific tool to investigate Complex Network Dynamics
• Interlayer antisynchronization in degree-biased duplex networks
• A novel framework to analyze complex network dynamics
• Desynchronization induced by time-varying network
• Percolation on interdependent networks with a fraction of antagonistic interactions
• Mathematical framework for breathing chimera states
• The spectral density of dense random networks and the breakdown of the Wigner semicircle law
• Multistability and anomalies in oscillator models of lossy power grids
• Optimal global synchronization of partially forced Kuramoto oscillators
• Dynamical complexity as a proxy for the network degree distribution
• Synchronization of persistent oscillations in spin systems with non-local dissipations
• Optimal Synchronization in Space
• The Boundaries of Synchronization in Oscillators Networks
• Dynamical Complexity in the C.elegans Neural Network
• Order parameter analysis of synchronization transitions on star networks
• Geometry, Topology and Simplicial Synchronization
• Generalized Synchronization of Coupled Chaotic Systems
• Physical networks as network-of-networks
• Aging in transport processes on networks with stochastic cumulative damage
• Model Reduction for the Kuramoto-Sakaguchi Model: The Importance of Non-entrained Rogue Oscillators
• Synchronization by Magnetostriction
• Statistically consistent coarse-grained simulations for critical phenomena in complex networks
• Dissipative nonequilibrium synchronization of topological edge states via self-oscillation
• Reconstructing directed networks for better synchronization
• Communicability Angles Reveal Critical Edges for Network Consensus Dynamics
• Driven synchronization in random networks of oscillators
• Symmetry-broken states on networks of coupled oscillators
• Synchronized chaos in networks of simple units
• Emergence and coherence of oscillations in star networks of stochastic excitable elements
• Reconstructing dynamical networks via feature ranking
• Sensitive Dependence of Optimal Network Dynamics on Network Structure
• Feedback-induced stationary localized patterns in networks of diffusively coupled bistable elements
• Enhancing network synchronization by phase modulation
• Tweaking Synchronisation by Link Addition
• Rare slips in fluctuating synchronized oscillator networks
• Ordinal methods for a characterization of evolving functional brain networks
• A general model of hierarchical fractal scale-free networks
• Collective dynamics on higher-order networks
• Concurrent enhancement of percolation and synchronization in adaptive networks
• Coarse Graining the Dynamics of Heterogeneous Oscillators in Networks with Spectral Gaps
• Extreme-value statistics of networks with inhibitory and excitatory couplings
• Phase synchronization between collective rhythms of fully locked oscillator groups
• Synaptic Plasticity and Spike Synchronisation in Neuronal Networks
• Symmetries and synchronization in multilayer random networks
• An integrative dynamical perspective for graph theory and the study of complex networks
• Collective oscillations of excitable elements: order parameters, bistability and the role of stochasticity
• A robust autoassociative memory with coupled networks of Kuramoto-type oscillators
• Multistability in lossy power grids and oscillator networks
• From the Kuramoto-Sakaguchi model to the Kuramoto-Sivashinsky equation
• Nonequilibrium criticality driven by Kardar-Parisi-Zhang fluctuations in the synchronization of oscillator lattices
• Complex Aperture Networks
• Cascade Failure in a Phase Model of Power Grids
• Predicting synchronized gene coexpression patterns from fibration symmetries in gene regulatory networks in bacteria
• Topological quantum synchronization of fractionalized spins
• Recovery time after localized perturbations in complex dynamical networks
• Impact of heterogeneous delays on cluster synchronization
• Entropic Causal Inference for Neurological Applications
• Synchronization on Effective Networks
• Collective Dynamics from Stochastic Thermodynamics
• Critical dynamics of the Kuramoto model on sparse random networks
• Finite Size Scaling in the Kuramoto Model
• Measuring the universal synchronization properties of coupled oscillators across the Hopf instability
• Synchronization dynamics on the EU and US power grids
• From random walks on networks to nonlinear diffusion
• Synchronization versus neighborhood similarity in complex networks of non-identical oscillators
• Sizing the length of complex networks
• Synchronization of a Self-Sustained Cold Atom Oscillator
• Adjoint-based phase reduction analysis of incompressible periodic flows
• Chaos in networks of coupled oscillators with multimodal natural frequency distributions
• Heterogeneity extends criticality
• Dynamic synchronization of a time-evolving optical network of chaotic oscillators
• Quantum synchronisation and clustering in chiral networks
• Symmetry-breaking mechanism for the formation of cluster chimera patterns
• Transient sequences in a hypernetwork generated by an adaptive network of spiking neurons
• Spontaneous Formation of Dynamical Groups in an Adaptive Networked System
• Nonlinear consensus on networks: equilibria, effective resistance and trees of motifs
• Statistical Analysis of Tipping Pathways in Agent-Based Models
• Synchronization of coupled metronomes on two layers
• Erosion of synchronization: Coupling heterogeneity and network structure
• Synchronization in the presence of time delays and inertia: Stability criteria
• Non-reciprocal interactions enhance heterogeneity
• Dynamics of multilayer networks with amplification
• Role of time scales and topology on the dynamics of complex networks
• Adversarial decision strategies in multiple network phased oscillators: the Blue-Green-Red Kuramoto-Sakaguchi model
• Collective frequency variation in network synchronization and reverse PageRank
• Dynamical robustness of complex networks subject to long-range connectivity
• Synchronization of moving integrate and fire oscillators
• Statistical complexity and connectivity relationship in cultured neural networks
• Suppression of synchronous spiking in two interacting populations of excitatory and inhibitory quadratic integrate-and-fire neurons
• Synchronization in Networks of Coupled Harmonic Oscillators with Stochastic Perturbation and Time Delays
• Variety of regimes of star-like networks of Henon maps
• Synchronization Invariance Under Network Structural Transformations
• Classical-driving-assisted quantum synchronization in non-Markovian environments
• Community structure revealed by phase locking
• Structural Inference of Networked Dynamical Systems with Universal Differential Equations
• Periodic orbits in the Ott-Antonsen manifold
• Measure synchronization in interacting Hamiltonian systems: A brief review
• Networks of noisy oscillators with correlated degree and frequency dispersion
• Multilayer modeling of adoption dynamics in energy demand management
• Structural and spectral properties of a family of deterministic recursive trees: Rigorous solutions
• Collective dynamics of phase-repulsive oscillators solves graph coloring problem
• Optimization of coupling and global collapse in diffusively coupled socio-ecological resource exploitation networks
• Finite-size scaling of geometric renormalization flows in complex networks
• Bounds of memory strength for power-law series
• Non-linear network dynamics with consensus-dissensus bifurcation
• Quenched mean-field theory for the majority-vote model on complex networks
• Extreme Fluctuations in Stochastic Network Coordination with Time Delays
• Subspace Decomposition for Graphon LQR: Applications to VLSNs of Harmonic Oscillators
• Hamiltonian control of Kuramoto oscillators
• Optimal Experimental Design for Uncertain Systems Based on Coupled Differential Equations
• On controlling networks of limit-cycle oscillators
• Role of assortativity in predicting burst synchronization using echo state network
• Persistence of chimera states and the challenge for synchronization in real-world networks
• Derivative-variable correlation reveals the structure of dynamical networks
• Effect of overlap on spreading dynamics on multiplex networks
• Evolutionary Subnetworks in Complex Systems
• Stationary patterns in star networks of bistable units: Theory and application to chemical reactions
• Stability of networks of delay-coupled delay oscillators
• On the pinning strategy of complex networks
• Influence of the topology on the dynamics of a complex network of HIV/AIDS epidemic models
• Synchronization transition of the second-order Kuramoto model on lattices
• Opinion Dynamics with Multi-Body Interactions
• Reduced-order adaptive synchronization in a chaotic neural network with parameter mismatch: A dynamical system vs. machine learning approach
• Dynamics of Minimal Networks of Limit Cycle Oscillators
• Extreme multistability in symmetrically coupled clocks
• Onset of Synchronization in Weighted Complex Networks: the Effect of Weight-Degree Correlation
• Optimal synchronization on strongly connected directed networks
• Random walks on networks with preferential cumulative damage: Generation of bias and aging
• Radial and circular synchronization clusters in extended starlike network of van der Pol oscillators
• Finite-time Correlations Boost Large Voltage-Angle Fluctuations in Electric Power Grids
• Algorithmic complexity of multiplex networks
• An efficient approach to suppress the negative role of contrarian oscillators in synchronization
• Phase transitions with infinitely many absorbing states in complex networks
• Analytic relationship of relative synchronizability to network structure and motifs
• Spectra of random networks in the weak clustering regime
• Phase and amplitude dynamics of coupled oscillator systems on complex networks
• Topological Complexity of Frictional Interfaces: Friction Networks
• Transmission of information and synchronization in a pair of coupled chaotic circuits: an experimental overview
• Random Walk with Memory on Complex Networks
• Inference of topology and the nature of synapses, and the flow of information in neuronal networks
• Symmetry and localization of quantum walk induced by extra link in cycles
• Rewiring hierarchical scale-free networks: Influence on synchronizability and topology
• Bifurcations in the Kuramoto model with external forcing and higher-order interactions
• Rank the spreading influence of nodes using dynamic Markov process
• Active XY model on a substrate: Density fluctuations and phase ordering
• Mobility-induced order in active XY spins on a substrate
• Periodic Coupling inhibits Second-order Consensus on Networks
• Synchronization conditions in the Kuramoto model and their relationship to seminorms
• Optimal and Approximate Solutions to Linear Quadratic Regulation of a Class of Graphon Dynamical Systems
• Spontaneous symmetry breaking and discontinuous phase transition for spreading dynamics in multiplex networks
• Variability in Fermi--Pasta--Ulam--Tsingou Arrays Prevents Recurrences
• Double phase transition of the Ising model in core-periphery networks
• iSIRA: Integrated Shift-Invert Residual Arnoldi Method for Graph Laplacian Matrices from Big Data
• Percolation of networks with directed dependency links
• Accelerating coordination in temporal networks by engineering the link order
• Social Diffusion and Global Drift on Networks
• Dynamical behaviours in time-delay systems with delayed feedback and digitized coupling
• Patterns of Emotional Blogging and Emergence of Communities: Agent-Based Model on Bipartite Networks
• Nucleation in scale-free networks
• Pulses of chaos synchronization in coupled map chains with delayed transmission
• Exact Response Theory and Kuramoto dynamics
• Control energy scaling in temporal networks
• Accelerating Optimal Experimental Design for Robust Synchronization of Uncertain Kuramoto Oscillator Model Using Machine Learning
• Synchronization of phase oscillators on the hierarchical lattice
• Radiative damping and synchronization in a graphene-based terahertz emitter
• Twisted states in low-dimensional hypercubic lattices
• Dynamics on Spatial Networks and the Effect of Distance Coarse Graining
• Universal bursty behavior in the air transportation system
• Tuning the Clustering Coefficient of Generalized Circulant Networks
• Quantum phase transitions in networks of Lipkin-Meshkov-Glick models
• Inferring synchronizability of networked heterogenous oscillators with machine learning
• The effect of distributed time-delays on the synchronization of neuronal networks
• Synchronization of Networked Jahn-Teller Systems in Circuit QED
• Synchronization of Network-Coupled Oscillators with Uncertain Dynamics
• A "Cellular Neuronal" Approach to Optimization Problems
• Effect of chaotic agent dynamics on coevolution of cooperation and synchronization
• Experimental implementation of maximally synchronizable networks
• Chimera-like States in Structured Heterogeneous Networks
• On the trend to global equilibrium for Kuramoto Oscillators
• Decreased resilience in power grids under dynamically induced vulnerabilities
• Exploring the Kibble-Zurek mechanism in a secondary bifurcation
• Optimal control of network-coupled subsystems: Spectral decomposition and low-dimensional solutions
• Geometric unfolding of synchronization dynamics on networks
• Critical parameters of the synchronisation's stability for coupled maps in regular graphs
• Optimizing synchronization in multiplex networks of phase oscillators
• Discontinuous Attractor Dimension at the Synchronization Transition of Time-Delayed Chaotic Systems
• Sample-to-sample fluctuations in real-network ensembles
• Enhancing synchronization in growing networks
• Small-amplitude synchronisation in driven Potts models
• Early detection of synchrony in coupled oscillator model
• Predicting the Onset of Quantum Synchronization Using Machine Learning
• A new dynamical model for solving rotation averaging problem
• Symmetry-driven network reconstruction through pseudobalanced coloring optimization
• Control of multidimensional systems on complex network
• Unevenness of Loop Location in Complex Networks
• Chimera states in a network-organized public goods game with destructive agents
• Symmetry and symmetry breaking in coupled oscillator communities
• Fast algorithm to identify cluster synchrony through fibration symmetries in large information-processing networks
• Group synchrony, parameter mismatches, and intragroup connections
• Discovering universal statistical laws of complex networks
• Influence of topology in the mobility enhancement of pulse-coupled oscillator synchronization
• Approximation methods for the stability of complete synchronization on duplex networks
• Networks of reinforced stochastic processes: asymptotics for the empirical means
• Kardar-Parisi-Zhang universality class in the synchronization of oscillator lattices with time-dependent noise
• Analytic solution to space-fractional Fokker-Planck equations for tempered-stable Lévy distributions with spatially linear, time-dependent drift
• Pulsed chaos synchronization in networks with adaptive couplings
• Impact of field heterogeneity on the dynamics of the forced Kuramoto model
• Kardar-Parisi-Zhang fluctuations in the synchronization dynamics of limit-cycle oscillators
• Collective dynamics of random Janus oscillator networks
• Aperiodic dynamics in a deterministic model of attitude formation in social groups
• Decoupling approximation robustly reconstructs directed dynamical networks
• Temporal Interaction and its Role in the Evolution of Cooperation
• Emergent information dynamics in many-body interconnected systems
• A perturbation-based approach to identifying potentially superfluous network constituents
• Social Network Heterogeneity Promotes Depolarization of Multidimensional Correlated Opinions
• Multiple structural transitions in interacting networks
• Small Worlds in Space: Synchronization, Spatial and Relational Modularity
• Stabilizing Stuart-Landau oscillators via time-varying networks
• Discordant synchronization patterns on directed networks of identical phase oscillators with attractive and repulsive couplings
• Characterizing cycle structure in complex networks
• The Hamiltonian Mean Field model: effect of network structure on synchronization dynamics
• On the reliable and efficient numerical integration of the Kuramoto model and related dynamical systems on graphs
• Feedback-induced desynchronization and oscillation quenching in a population of globally coupled oscillators
• Network evolution towards optimal dynamical performance
• Stability of Synchronized Motion in Complex Networks
• The Lifting Bifurcation Problem on Feed-Forward Networks
• Frequency Synchronization Induced by Frequency Detuning
• Thermodynamic Characterization of Synchronization-Optimized Oscillator-Networks
• Scaling and synchronization in a ring of diffusively coupled nonlinear oscillators
• Variability of collective dynamics in random tree networks of strongly-coupled stochastic excitable elements
• Quasi-symmetries in complex networks: a dynamical model approach
• Synchronization in populations of sparsely connected pulse-coupled oscillators
• Complexity and asymptotic stability in the process of biochemical substance exchange in a coupled ring of cells
• Node Diversification in Complex Networks by Decentralized Coloring
• Complexity and irreducibility of dynamics on networks of networks
• Global Topological Dirac Synchronization
• Guaranteed Performance Leader-follower Control for Multi-agent Systems with Linear IQC-Constrained Coupling
• Huygens' synchronization experiment revisited: Luck or skill?
• Control of Hierarchical Networks by Coupling to an External Chaotic System
• Topological phase transition in the periodically forced Kuramoto model
• Modeling international crisis synchronization in the World Trade Web
• Influence of cumulative damage on synchronization of Kuramoto oscillators on networks
• Neuromodulation Influences Synchronization and Intrinsic Read-out
• Synchronization for Networks of Globally Coupled Maps in the Thermodynamic Limit
• Meso-scale obstructions to stability of 1D center manifolds for networks of coupled differential equations with symmetric Jacobian
• Studying power-grid synchronization with incremental refinement of model heterogeneity
• Eigenvector localization in hypergraphs: pair-wise vs higher-order links
• Broadcasting solutions on networked systems of phase oscillators
• Emergence of chaotic cluster synchronization in heterogeneous networks
• Spectral Graph Complexity
• Detection of Functional Communities in Networks of Randomly Coupled Oscillators Using the Dynamic-Mode Decomposition
• Target Patterns in a 2-D Array of Oscillators with Nonlocal Coupling
• Synchronization transitions in adaptive simplicial complexes with cooperative and competitive dynamics
• Synchronization in an evolving network
• Coherence and incoherence collective behavior in financial market
• Degree heterogeneity in spatial networks with total cost constraint
• Global and Partial Phase Synchronizations in Arrays of Piecewise Linear Time-Delay Systems
• Concurrent formation of nearly synchronous clusters in each intertwined cluster set with parameter mismatches
• Two network Kuramoto-Sakaguchi model under tempered stable Lévy noise
• Stochastic resetting in a networked multiparticle system with correlated transitions
• Detectability Conditions and State Estimation for Linear Time-Varying and Nonlinear Systems
• Tristable and multiple bistable activity in complex random binary networks of two-state units
• Effect of Burstiness on the Air Transportation System
• Organic Design of Massively Distributed Systems: A Complex Networks Perspective
• Moderate Higher-Order Interactions Enhance Stability While Preserving Basin Structure
• Large and small fluctuations in oscillator networks from heterogeneous and correlated noise
• How does degree heterogeneity affect nucleation of Ising model on complex networks?
• Universal dynamics of spatiotemporal entrainment with phase symmetry
• Invariant Synchrony and Anti-Synchrony Subspaces of Weighted Networks
• Towards a robust algorithm to determine topological domains from colocalization data
• Transient dynamics of pulse-coupled oscillators with nonlinear charging curves
• On the Landscape of Synchronization Networks: A Perspective from Nonconvex Optimization
• Quantum Superexponential Oscillator
• Symmetry-based coarse-graining of evolved dynamical networks
• Binary Mixtures of Locally Coupled Mobile Oscillators
• Mesoscopic model reduction for the collective dynamics of sparse coupled oscillator networks
• Global Practical Node and Edge Synchronization in Kuramoto Networks: A Submodular Optimization Framework
• Synchronization in nonlinear oscillators with conjugate coupling
• Extracting phase coupling functions between collectively oscillating networks directly from time-series data
• Expander graphs are globally synchronizing
• How to grow an oscillator network with enhanced synchronization
• Topologically-induced suppression of explosive synchronization
• Desynchronizing two oscillators while stimulating and observing only one
• Emergence of metastability in frustrated oscillatory networks: the key role of hierarchical modularity
• Antifragility and response to damage in the synchronization of oscillators on networks
• Dynamical equivalence between resonant translocation of a polymer chain and diversity-induced resonance
• Potts model with q=3 and 4 states on directed Small-World network
• Quantum synchronization in an all-optical stroboscopic quantum simulator
• Influence of coupling symmetries and noise on the critical dynamics of synchronizing oscillator lattices
• Coarse-grained Monte Carlo simulations of the phase transition of Potts model on weighted networks
• Drifting states and synchronization induced chaos in autonomous networks of excitable neurons
• Network heterogeneity and node capacity lead to heterogeneous scaling of fluctuations in random walks on graphs
• Coexistence of exponentially many chaotic spin-glass attractors
• Computing the Threshold of the Influence of Intercellular Nanotubes on Cell-to-Cell Communication Integrity
• Construction of the Lyapunov spectrum in a chaotic system displaying phase synchronization
• Modeling the dynamics and control of power systems with high share of renewable energies
• A machine learning approach to investigate regulatory control circuits in bacterial metabolic pathways
• Explosive synchronization in temporal networks: A comparative study
• Topologically protected synchronization in networks
• Data assimilation for networks of coupled oscillators: Inferring unknown model parameters from partial observations
• Efficient parameter inference in networked dynamical systems via steady states: A surrogate objective function approach integrating mean-field and nonlinear least squares
• On the location and the strength of controllers to desynchronize coupled Kuramoto oscillators
• Signal metrics analysis of oscillatory patterns in bacterial multi-omic networks
• Asymptotically inspired moment-closure approximation for adaptive networks
• Theory of Interface: Category Theory, Directed Networks and Evolution of Biological Networks
• Asymptotic periodicity in networks of degrade-and-fire oscillators
• Reconstruction of evolved dynamic networks from degree correlations
• Finite-size scaling and dynamics in a two-dimensional lattice of identical oscillators with frustrated couplings
• Quantum magnetism on small-world networks
• Finding Non-Zero Stable Fixed Points of the Weighted Kuramoto model is NP-hard
• Networks with asymmetric inputs: lattice of synchrony subspaces
• The spark of synchronization in heterogeneous networks of chaotic maps
• Cooperative output regulation of multi-agent network systems with dynamic edges
• Optimal interaction functions realizing higher-order Kuramoto dynamics with arbitrary limit-cycle oscillators
• Functional brain networks: great expectations, hard times, and the big leap forward
• Fractals in the Nervous System: conceptual Implications for Theoretical Neuroscience
• Crossover from mean-field to $2d$ Directed Percolation in the contact process
• Synchronization of Chaos
• Independent Noise Synchronizing Networks of Oscillator Networks
• Can Spatiality Promote Diversity?
• Emergent synchrony in oscillator networks with adaptive arbitrary-order interactions
• Revisiting asymptotic periodicity in networks of degrade-and-fire oscillators
• Exact rank-reduction of network models
• Commutative Monoid Formalism for Weighted Coupled Cell Networks and Invariant Synchrony Patterns
• Large deviation and anomalous fluctuations scaling in degree assortativity on configuration networks
• Networks of reinforced stochastic processes: a complete description of the first-order asymptotics
• End-coupled random lasers: a basis for artificial neural networks
• One dimensional singular Cucker-Smale model: uniform-in-time mean-field limit and contractivity
• Reaction-diffusion on random spatial networks with scale-free jumping rates via effective medium theory
• Phase Model with Feedback Control for Power Grids
• Notes on Resonant and Synchronized States in Complex Networks
• Networks of planar Hamiltonian systems
• Mean-field approach for frequency synchronization in complex networks of two oscillator types
• Multiple predator based capture process on complex networks
• Diffusion and synchronization dynamics reveal the multi-scale patterns of spatial segregation
• Adversarial control of synchronization in complex oscillator networks
• Designing topological cluster synchronization patterns with the Dirac operator
• Dynamics of Cluster Synchronisation in Modular Networks: Implications for Structural and Functional Networks
• Transcript-based estimators for characterizing interactions
• Effects of long-range links on metastable states in a dynamic interaction network
• Controlling Complex Systems
• Data-driven stochastic modeling of coarse-grained dynamics with finite-size effects using Langevin regression
• Dynamical leaps due to microscopic changes in multiplex networks
• Coprime networks of the composite numbers: pseudo-randomness and synchronizability
• Evolution of robustness in growing random networks
• Semicontraction and Synchronization of Kuramoto-Sakaguchi Oscillator Networks
• Coevolutionary Dynamics with Global Fields
• On the Critical Coupling of the Finite Kuramoto Model on Dense Networks
• Explosive Synchronization in Multilayer Dynamically Dissimilar Networks
• Interacting non-linear reinforced stochastic processes: synchronization and no-synchronization
• Adaptive Diffusion Processes of Time-Varying Local Information on Networks
• Noise stability of synchronization and optimal network structures
• Order parameter allows classification of planar graphs based on balanced fixed points in the Kuramoto model
• Small World Property of a Rock Joint(Complexity of Frictional Interfaces: A Complex Network Perspective)
• Synchronization and extinction in a high-infectivity spatial SIRS with long-range links
• Understanding the enhanced synchronization of delay-coupled networks with fluctuating topology
• Nonlinear Modal Decoupling of Multi-Oscillator Systems with Applications to Power Systems
• Macroscopic Models for Networks of Coupled Biological Oscillators
• Growing Networks with Super-Joiners
• Non-Markovian Character in Human Mobility: Online and Offline
• Nonlinear waves on circle networks with excitable nodes
• Nonextensive analysis on the local structure entropy of complex networks
• Measure the similarity of nodes in the complex networks
• Network community detection via iterative edge removal in a flocking-like system
• Locating influential nodes via dynamics-sensitive centrality
• Probability of Stability of Synchronization in Random Networks of Mismatched Oscillators
• Universal interface fluctuations in the contact process
• Networks of reinforced stochastic processes: probability of asymptotic polarization and related general results
• Percolation critical exponents in cluster kinetics of pulse-coupled oscillators
• Phase reduction analysis of traveling breathers in reaction--diffusion systems
• Partitioning networks into clusters of synchronized nodes via the message-passing algorithm: an unbiased scalable approach
• Abnormal Synchronizing Path of Delay-coupled Chaotic Oscillators on the Edge of Stability
• Maximizing the algebraic connectivity in multilayer networks with arbitrary interconnections
• Protein Folding/Unfolding Phenomenon is originated by Synchronization/Desynchronization of Instantaneously Induced Oscillating Dipoles. A Hypothesis
• Path-dependent Dynamics Induced by Rewiring Networks of Inertial Oscillators
• Regular and irregular modulation of frequencies in limit cycle oscillator networks
• On the root count of algebraic Kuramoto equations in cycle networks with uniform coupling
• From Spatial to Spectral: Network Renormalization via Dynamical Correlations
• Tsallis entropy of complex networks
• Emergent togetherness in collaborative dance improvisation: neural and motor synchronization reveal a coupling-decoupling paradox
• Collision-induced coherent dynamics
• Impact of Dynamic Interactions on Multi-Scale Analysis of Community Structure in Networks
• Trade-Off Between Multiplicity and Specificity in the Inter-layer Connectivity of non-identical Multilayer Networks
• Enhancement of Network Synchronizability via Two Oscillatory System
• Evolutionary design of non-frustrated networks of phase-repulsive oscillators
• Emergence of a spectral gap in a class of random matrices associated with split graphs
• Effective synchronization amid noise-induced chaos
• On the extremal spectral properties of random graphs
• Discrete structure of the brain rhythms
• Susceptibility of power grids to input fluctuations
• Spatio-Temporal Graphical Counterfactuals: An Overview
• Stability Analysis of Network of Similar-Plants via Feedback Network
• Observability of Nonlinear Complex Networks in the Presence of Symmetries: A Graphical Approach
• Collective dynamics in a laser-pumped mixture of two atomic ensembles
• Mean-field theory of vector spin models on networks with arbitrary degree distributions
• Spectral Gradient Iterative Edge Attack for Synchronization Suppression in Complex Networks
• Connecting Hodge and Sakaguchi-Kuramoto: a mathematical framework for coupled oscillators on simplicial complexes
• The Impact of Network Flows on Community Formation in Models of Opinion Dynamics
• Quantum fingerprints of self-organization in spin chains coupled to a Kuramoto model
• Intrinsic Resonance depends on Network Size of Coupled-Delayed Interacting Oscillators
• Synchronization of nonlinearly coupled Stuart-Landau oscillators on networks
• Physical Oscillator Model for Supercomputing
• Synchronization transition in ensemble of coupled phase oscillators with coherence-induced phase correction
• Application of semidefinite programming to maximize the spectral gap produced by node removal
• A hybrid multiscale coarse-grained method for dynamics on complex networks
• Leader-follower Tracking Control with Guaranteed Consensus Performance for Interconnected Systems with Linear Dynamic Uncertain Coupling
• Different roles for inhibition in the rhythm-generating respiratory network
• Dissimilarity between synchronization processes on networks
• Emergence of solitary and chimera states in adaptive pendulum networks under diverse learning rules
• Theory of synchronisation and pattern formation on time varying networks
• Comparison of different spike train synchrony measures regarding their robustness to erroneous data from bicuculline induced epileptiform activity
• A stylised view on structural and functional connectivity in dynamical processes in networks
• Opportunities and challenges in partitioning the graph measure space of real-world networks
• Edges of inter-layer synchronization in multilayer networks with time-switching links
• Analytical foundation for adversarial synchronization control in oscillator networks
• A Distributed Optimization Scheme for State Estimation of Nonlinear Networks with Norm-bounded Uncertainties
• Interplay between Network Topology and Dynamics in Neural Systems
• Oscillatory states, standing waves, and additional synchronized clusters in networks of second-order oscillators: uncovering the role of inertia
• A convex-geometric framework for fully phase-locked states in the finite Kuramoto model
• Control technique for synchronization of selected nodes in directed networks
• Optimal cost tuning of frustration: Achieving desired states in the Kuramoto-Sakaguchi model
• On the efficiency of pairwise Hamiltonian control to desynchronize the higher-order Kuramoto model
• Synchronization optimized networks for coupled nearly identical oscillators and their structural analysis
• Dynamics and Synchronization of Boundary Coupled FitzHugh-Nagumo Neural Networks
• Transition to congestion in communication/computation networks: from ideal to realistic resource allocation via Montecarlo simulations