Low Dimensional Behavior of Large Systems of Globally Coupled Oscillators

Abstract

It is shown that, in the infinite size limit, certain systems of globally coupled phase oscillators display low dimensional dynamics. In particular, we derive an explicit finite set of nonlinear ordinary differential equations for the macroscopic evolution of the systems considered. For example, an exact, closed form solution for the nonlinear time evolution of the Kuramoto problem with a Lorentzian oscillator frequency distribution function is obtained. Low dimensional behavior is also demonstrated for several prototypical extensions of the Kuramoto model, and time-delayed coupling is also considered.

resubmission of Tex files

References in corpus (11)

• Time Delay in the Kuramoto Model of Coupled Oscillators
• Synchronization of two interacting populations of oscillators
• Amplitude Expansions for Instabilities in Populations of Globally-Coupled Oscillators
• Synchronization in networks of networks: the onset of coherent collective behavior in systems of interacting populations of heterogeneous oscillators
• Slow Switching in Globally Coupled Oscillators: Robustness and Occurrence through Delayed Coupling
• Synchronization in a System of Globally Coupled Oscillators with Time Delay
• The Spectrum of the Partially Locked State for the Kuramoto Model
• Averaged equations for Josephson junction series arrays with LRC load
• External Periodic Driving of Large Systems of Globally Coupled Phase Oscillators
• Time delay in the Kuramoto model with bimodal frequency distribution
• Strong Effects of Network Architecture in the Entrainment of Coupled Oscillator Systems

Cited by in corpus (383)

• Networks beyond pairwise interactions: structure and dynamics
• Chimera states: Coexistence of coherence and incoherence in networks of coupled oscillators
• Spontaneous synchrony in power-grid networks
• Non-reciprocal phase transitions
• Long Time Evolution of Phase Oscillator Systems
• Explosive transitions in complex networks' structure and dynamics: percolation and synchronization
• Macroscopic description for networks of spiking neurons
• Exact Results for the Kuramoto Model with a Bimodal Frequency Distribution
• Higher-order interactions in complex networks of phase oscillators promote abrupt synchronization switching
• Abrupt Desynchronization and Extensive Multistability in Globally Coupled Oscillator Simplices
• Coupling functions: Universal insights into dynamical interaction mechanisms
• Partially integrable dynamics of hierarchical populations of coupled oscillators
• Solvable Model of Spiral Wave Chimeras
• Understanding the dynamics of biological and neural oscillator networks through exact mean-field reductions: a review
• Chimera states in heterogeneous networks
• Phase oscillators with global sinusoidal coupling evolve by Mobius group action
• Explosive Phenomena in Complex Networks
• Stability diagram for the forced Kuramoto model
• Chimeras in networks with purely local coupling
• Conformists and contrarians in a Kuramoto model with identical natural frequencies
• Hysteretic transitions in the Kuramoto model with inertia
• Spontaneous Synchrony Breaking
• Controlling unstable chaos: Stabilizing chimera states by feedback
• Solitary state at the edge of synchrony in ensembles with attractive and repulsive interaction
• Low-dimensional dynamics of populations of pulse-coupled oscillators
• Self-Emerging and Turbulent Chimeras in Oscillator Chains
• Higher-order simplicial synchronization of coupled topological signals
• Chimeras in networks of planar oscillators
• Chimera states on a flat torus
• Control of coupled oscillator networks with application to microgrid technologies
• Frustrated hierarchical synchronization and emergent complexity in the human connectome network
• Chimera states in time-varying complex networks
• Symmetric States Requiring System Asymmetry
• Dynamics of noisy oscillator populations beyond the Ott-Antonsen ansatz
• Cluster Synchrony in Systems of Coupled Phase Oscillators with Higher-Order Coupling
• A Universal Route to Explosive Phenomena
• Chimera states in networks of phase oscillators: the case of two small populations
• Firing rate equations require a spike synchrony mechanism to correctly describe fast oscillations in inhibitory networks
• Continuous versus Discontinuous Transitions in the $D$-Dimensional Generalized Kuramoto Model: Odd $D$ is Different
• External Periodic Driving of Large Systems of Globally Coupled Phase Oscillators
• Basins of Attraction for Chimera States
• A Tweezer for Chimeras in Small Networks
• Stationary and Traveling Wave States of the Kuramoto Model with an Arbitrary Distribution of Frequencies and Coupling Strengths
• Existence of hysteresis in the Kuramoto model with bimodal frequency distributions
• Comment on "Long Time Evolution of Phase Oscillator Systems" [Chaos 19,023117 (2009), arXiv:0902.2773]
• Bistable Chimera Attractors on a Triangular Network of Oscillator Populations
• Chimeras in a Network of Three Oscillator Populations with Varying Network Topology
• The nonlinear heat equation on W-random graphs
• Noise-Induced Synchronization of a Large Population of Globally Coupled Nonidentical Oscillators
• Collective dynamics of swarmalators with higher-order interactions
• Higher-order interactions promote chimera states
• Anticipating synchronization with machine learning
• The Kuramoto Model with Time-Varying Parameters
• Invariant submanifold for series arrays of Josephson junctions
• Collective behaviour of swarmalators on a 1D ring
• Hierarchical Synchrony of Phase Oscillators in Modular Networks
• Critical behavior of the relaxation rate, the susceptibility, and a pair correlation function in the Kuramoto model on scale-free networks
• From quasiperiodic partial synchronization to collective chaos in populations of inhibitory neurons with delay
• Chaos in Symmetric Phase Oscillator Networks
• Chimera states in two-dimensional networks of locally coupled oscillators
• Phase resetting of collective rhythm in ensembles of oscillators
• Macroscopic phase resetting-curves determine oscillatory coherence and signal transfer in inter-coupled neural circuits
• On the Concept of Dynamical Reduction : The Case of Coupled Oscillators
• Chimera states in two populations with heterogeneous phase-lag
• Heterogeneity of time delays determines synchronization of coupled oscillators
• Glassy states and superrelaxation in populations of coupled phase oscillators
• Connecting the Kuramoto Model and the Chimera State
• Collective modes of coupled phase oscillators with delayed coupling
• Collective dynamical response of coupled oscillators with any network structure
• Non-universal results induced by diversity distribution in coupled excitable systems
• Perspectives on adaptive dynamical systems
• Noise-Induced Synchronization, Desynchronization, and Clustering in Globally Coupled Nonidentical Oscillators
• Sync and swarm: solvable model of non-identical swarmalators
• Exact mean-field theory explains the dual role of electrical synapses in collective synchronization
• Spontaneous synchronization of coupled oscillator systems with frequency adaptation
• A reduction methodology for fluctuation driven population dynamics
• Exact neural mass model for synaptic-based working memory
• Kuramoto model for excitation-inhibition-based oscillations
• Mean Field and Mean Ensemble Frequencies of a System of Coupled Oscillators
• Dynamics of a large system of spiking neurons with synaptic delay
• Shear diversity prevents collective synchronization
• Synchronization and spatial patterns in forced swarmalators
• An exact firing rate model reveals the differential effects of chemical versus electrical synapses in spiking networks
• The changing notion of chimera states, a critical review
• Mean field theory of assortative networks of phase oscillators
• Approximate solution to the stochastic Kuramoto model
• Finite-size-induced transitions to synchrony in oscillator ensembles with nonlinear global coupling
• Center manifold reduction for large populations of globally coupled phase oscillators
• Global attractor and asymptotic dynamics in the Kuramoto model for coupled noisy phase oscillators
• The oscillating two-cluster chimera state in non-locally coupled phase oscillators
• A next generation neural field model: The evolution of synchrony within patterns and waves
• Phase synchronization between collective rhythms of globally coupled oscillator groups: noiseless non-identical case
• Kuramoto dynamics in Hamiltonian systems
• Ott-Antonsen attractiveness for parameter-dependent oscillatory networks
• Bifurcations and singularities for coupled oscillators with inertia and frustration
• Model reduction for networks of coupled oscillators
• Heterogeneous nucleation in finite size adaptive dynamical networks
• Spectrum of extensive multiclusters in the Kuramoto model with higher-order interactions
• Chaos in Kuramoto oscillator networks
• Symmetry-independent stability analysis of synchronization patterns
• Coexistence of fast and slow gamma oscillations in one population of inhibitory spiking neurons
• Collective mode reductions for populations of coupled noisy oscillators
• Persistent chimera states in nonlocally coupled phase oscillators
• Low-dimensional behavior of Kuramoto model with inertia in complex networks
• Generating macroscopic chaos in a network of globally coupled phase oscillators
• Low Dimensional Description of Pedestrian-Induced Oscillation of the Millennium Bridge
• Dynamics and Pattern Formation in Large Systems of Spatially-Coupled Oscillators with Finite Response Times
• Interplay of coupling and common noise at the transition to synchrony in oscillator populations
• The Kuramoto model of coupled oscillators with a bi-harmonic coupling function
• Solvable model of the collective motion of heterogeneous particles interacting on a sphere
• Complex macroscopic behavior in systems of phase oscillators with adaptive coupling
• Hyperbolic Geometry of Kuramoto Oscillator Networks
• Low-Dimensional Dynamics for Higher Order Harmonic Globally Coupled Phase Oscillator Ensemble
• Bumps and Oscillons in Networks of Spiking Neurons
• Collective dynamics of heterogeneously and nonlinearly coupled phase oscillators
• Non-reciprocal frustration: time crystalline order-by-disorder phenomenon and a spin-glass-like state
• Structure of Cell Networks Critically Determines Oscillation Regularity
• Explosive synchronization with partial degree-frequency correlation
• Synchronization of phase oscillators on complex hypergraphs
• Deeper but smaller: Higher-order interactions increase linear stability but shrink basins
• Coherent oscillations in balanced neural networks driven by endogenous fluctuations
• Self-sustained irregular activity in an ensemble of neural oscillators
• Collective phase description of globally coupled excitable elements
• Solitary States and Partial Synchrony in Oscillatory Ensembles with Attractive and Repulsive Interactions
• Complexity Reduction Ansatz for Systems of Interacting Orientable Agents: Beyond The Kuramoto Model
• Chimera patterns in the Kuramoto-Battogtokh model
• Volcano transition in a solvable model of oscillator glass
• Exact finite-dimensional description for networks of globally coupled spiking neurons
• Effective potential approach to hybrid synchronization transitions
• Dynamics of multifrequency oscillator communities
• Synchronization of coupled active rotators by common noise
• Cross frequency coupling in next generation inhibitory neural mass models
• Synchronization in the Kuramoto model in presence of stochastic resetting
• Synchrony-induced modes of oscillation of a neural field model
• Multiscale Dynamics in Communities of Phase Oscillators
• Synchronization scenarios in the Winfree model of coupled oscillators
• Higher-order interactions induce anomalous transitions to synchrony
• Phase synchronization between collective rhythms of globally coupled oscillator groups: noisy identical case
• Critical Switching in Globally Attractive Chimeras
• Optimal synchronization of Kuramoto oscillators: a dimensional reduction approach
• Modeling the Network Dynamics of Pulse-Coupled Neurons
• Collective synchronization in the presence of reactive coupling and shear diversity
• Dirac synchronization is rhythmic and explosive
• Frequency assortativity can induce chaos in oscillator networks
• Is the Ott-Antonsen manifold attracting?
• Moving bumps in theta neuron networks
• Dynamics of phase oscillators in the Kuramoto model with generalized frequency-weighted coupling
• Excitable elements controlled by noise and network structure
• Collective phase dynamics of globally coupled oscillators: Noise-induced anti-phase synchronization
• Model reduction for Kuramoto models with complex topologies
• Population spiking and bursting in next generation neural masses with spike-frequency adaptation
• Synchrony suppression in ensembles of coupled oscillators via adaptive vanishing feedback
• Generalized splay states in phase oscillator networks
• The mathematics of asymptotic stability in the Kuramoto model
• Effects of non-resonant interaction in ensembles of phase oscillators
• Linked and knotted chimera filaments in oscillatory systems
• Cyclops states in repulsive Kuramoto networks: the role of higher-order coupling
• Multiplexing induced explosive synchronization in Kuramoto oscillators with inertia
• Dynamics of a population of oscillatory and excitable elements
• Experimental Study of Synchronization of Coupled Electrical Self-Oscillators and Comparison to the Sakaguchi-Kuramoto model
• Ott-Antonsen ansatz is the only admissible truncation of a circular cumulant series
• Cluster singularity: the unfolding of clustering behavior in globally coupled Stuart-Landau oscillators
• First-order phase transitions in the Kuramoto model with compact bimodal frequency distributions
• Phase diagram for the Kuramoto model with van Hemmen interactions
• Transition to Collective Oscillations in Finite Kuramoto Ensembles
• Threefold way to the dimension reduction of dynamics on networks: an application to synchronization
• Dynamics of weakly inhomogeneous oscillator populations: Perturbation theory on top of Watanabe-Strogatz integrability
• Macroscopic Dynamics of Neural Networks with Heterogeneous Spiking Thresholds
• Two Scenarios for the Onset and Suppression of Collective Oscillations in Heterogeneous Populations of Active Rotators
• Star-type oscillatory networks with generic Kuramoto-type coupling: a model for "Japanese drums synchrony"
• Kuramoto model for populations of quadratic integrate-and-fire neurons with chemical and electrical coupling
• Chimera states in small disordered optomechanical arrays
• Low-dimensional description for ensembles of identical phase oscillators subject to Cauchy noise
• Multistability in coupled oscillator systems with higher-order interactions and community structure
• Coherence resonance in influencer networks
• Low Dimensional Dynamics of the Kuramoto Model with Rational Frequency Distributions
• Repulsively Coupled Kuramoto-Sakaguchi Phase Oscillators Ensemble Subject to Common Noise
• The Kuramoto model with distributed shear
• Hierarchy of exact low-dimensional reductions for populations of coupled oscillators
• Self-consistent Method and Steady States of Second-order Oscillators
• Generic criterion for explosive synchronization in heterogeneous phase oscillator populations
• Coupled networks and networks with bimodal frequency distributions are equivalent
• Enlarged Kuramoto Model: Secondary Instability and Transition to Collective Chaos
• Ott-Antonsen ansatz for the D-dimensional Kuramoto model: a constructive approach
• Symmetry breaking in two interacting populations of quadratic integrate-and-fire neurons
• Landau damping to partially locked states in the Kuramoto model
• Echo Phenomena in Large Systems of Coupled Oscillators
• Generalized frustration in the multidimensional Kuramoto model
• Observing Microscopic Transitions from Macroscopic Bursts: Instability-Mediated Resetting in the Incoherent Regime of the $D$-dimensional Generalized Kuramoto Model
• Global dynamics of oscillator populations under common noise
• From phase to amplitude oscillators
• Breathing multichimera states in nonlocally coupled phase oscillators
• Self-organized explosive synchronization in complex networks: Emergence of synchronization bombs
• Emergent excitability in adaptive networks of non-excitable units
• Stability of phase difference trajectories of networks of Kuramoto oscillators with time-varying couplings and intrinsic frequencies
• Eigenvector-based analysis of cluster synchronization in general complex networks of coupled chaotic oscillators
• Pattern selection in a ring of Kuramoto oscillators
• Synchronization Transition in the Kuramoto Model with Colored Noise
• Desynchronization induced by time-varying network
• Mathematical framework for breathing chimera states
• Optimal global synchronization of partially forced Kuramoto oscillators
• Mean field approximation of two coupled populations of excitable units
• Symmetry breaking yields chimeras in two small populations of Kuramoto-type oscillators
• Amplification of explosive width in complex networks
• Low-dimensional dynamics of phase oscillators driven by Cauchy noise
• Interplay of the mechanisms of synchronization by common noise and global coupling for a general class of limit-cycle oscillators
• Mean-field equations for neural populations with $q$-Gaussian heterogeneities
• Model Reduction for the Kuramoto-Sakaguchi Model: The Importance of Non-entrained Rogue Oscillators
• On synchronization in Kuramoto models on spheres
• Driven synchronization in random networks of oscillators
• Order parameter analysis of synchronization transitions on star networks
• Self adaptation of chimera states
• Enhancing network synchronization by phase modulation
• Stable and flexible system for glucose homeostasis
• Collective dynamics on higher-order networks
• Integrability of a globally coupled complex Riccati array: quadratic integrate-and-fire neurons, phase oscillators and all in between
• Matrix coupling and generalized frustration in Kuramoto oscillators
• Average activity of excitatory and inhibitory neural populations
• Phase synchronization between collective rhythms of fully locked oscillator groups
• Rare slips in fluctuating synchronized oscillator networks
• Stability of rotatory solitary states in Kuramoto networks with inertia
• From the Kuramoto-Sakaguchi model to the Kuramoto-Sivashinsky equation
• Exact finite-dimensional reduction for a population of noisy oscillators and its link to Ott-Antonsen and Watanabe-Strogatz theories
• Universal scaling and phase transitions of coupled phase oscillator populations
• Synchronization transitions in Kuramoto networks with higher-mode interaction
• Kuramoto model subject to subsystem resetting: How resetting a part of the system may synchronize the whole of it
• Symmetries and synchronization in multilayer random networks
• The Kuramoto model in presence of additional interactions that break rotational symmetry
• Effective low-dimensional dynamics of a mean-field coupled network of slow-fast spiking lasers
• Nonstandard transitions in the Kuramoto model: A role of asymmetry in natural frequency distributions
• Multifaceted dynamics of Janus oscillator networks
• Critical dynamics of the Kuramoto model on sparse random networks
• Collective Dynamics from Stochastic Thermodynamics
• Macroscopic behavior of populations of quadratic integrate-and-fire neurons subject to non-Gaussian white noise
• Transition to Synchrony in a Three-Dimensional Swarming Model with Helical Trajectories
• Chimera states in systems of nonlocal nonidentical phase-coupled oscillators
• Dynamics of multi-frequency oscillator ensembles with resonant coupling
• Attracting Poisson Chimeras in Two-population Networks
• Chaos in networks of coupled oscillators with multimodal natural frequency distributions
• Locking and regularisation of chimeras by periodic forcing
• Synchronization in the random field Kuramoto model on complex networks
• Relationships between the Distribution of Watanabe-Strogatz Variables and Circular Cumulants for Ensembles of Phase Elements
• Tiered synchronization in coupled oscillator populations with interaction delays and higher-order interactions
• Dynamics of two populations of phase oscillators with different frequency distributions
• Noise induced swarming of active particles
• Suppression of synchronous spiking in two interacting populations of excitatory and inhibitory quadratic integrate-and-fire neurons
• Synchronization of Coupled Kuramoto Oscillators under Resource Constraints
• The Winfree model with heterogeneous phase-response curves: Analytical results
• Synchronization transitions on connectome graphs with external force
• Stability Diagram, Hysteresis, and Critical Time Delay and Frequency for the Kuramoto Model with Heterogeneous Interaction Delays
• Collective frequency variation in network synchronization and reverse PageRank
• Relaxation time of the global order parameter on multiplex networks: the role of interlayer coupling in Kuramoto oscillators
• Continuum limits of coupled oscillator networks depending on multiple sparse graphs
• Bifurcations in the time-delayed Kuramoto model of coupled oscillators: Exact results
• Complex behavior in chains of nonlinear oscillators
• Noise-induced stabilization of collective dynamics
• Onset of synchronization in networks of second-order Kuramoto oscillators with delayed coupling: Exact results and application to phase-locked loops
• Emergence of second coherent regions for breathing chimera states
• Synchronization transitions in ensembles of noisy oscillators with bi-harmonic coupling
• Periodic orbits in the Ott-Antonsen manifold
• Cooperative behavior between oscillatory and excitable units: the peculiar role of positive coupling-frequency correlations
• Coupled Moebius Maps as a Tool to Model Kuramoto Phase Synchronization
• Synchronization Behavior in a Ternary Phase Model
• Synchronization transition of the second-order Kuramoto model on lattices
• Volcano transition in populations of phase oscillators with random nonreciprocal interactions
• Bifurcations in the Kuramoto model with external forcing and higher-order interactions
• The lower bound of the network connectivity guaranteeing in-phase synchronization
• Complexified Synchrony
• Collective dynamics in the presence of finite-width pulses
• Influence of Asymmetric Parameters in Higher-Order Coupling With Bimodal Frequency Distribution
• Exploring hyper-parameter spaces of neuroscience models on high performance computers with Learning to Learn
• Continuous and discontinuous transitions to synchronization
• Graphop Mean-Field Limits and Synchronization for the Stochastic Kuramoto Model
• Relaxation dynamics of the Kuramoto model with uniformly distributed natural frequencies
• Phase diagram of noisy systems of coupled oscillators with a bimodal frequency distribution
• Order parameter expansion study of synchronous firing induced by quenched noise in the active rotator model
• Solitary synchronization waves in distributed oscillators populations
• Chimera-like States in Structured Heterogeneous Networks
• Collective Phase Chaos in the Dynamics of Interacting Oscillator Ensembles
• The effects of within-neuron degree correlations in networks of spiking neurons
• Impact of field heterogeneity on the dynamics of the forced Kuramoto model
• A general coupled nonlinear oscillator model for event-related (de)synchronization
• Manipulating phases in many-body interacting systems with subsystem resetting
• Global and Local Reduced Models for Interacting, Heterogeneous Agents
• Symmetry and symmetry breaking in coupled oscillator communities
• Circular Cumulant Reductions for Macroscopic Dynamics of Kuramoto Ensemble with Multiplicative Intrinsic Noise
• Möbius transformations and electronic transport properties of large disorderless networks
• Circular cumulant reductions for macroscopic dynamics of oscillator populations with non-Gaussian noise
• Heteroclinic Switching between Chimeras in a Ring of Six Oscillator Populations
• Collective dynamics of random Janus oscillator networks
• Cross-scale excitability in networks of synaptically-coupled quadratic integrate-and-fire neurons
• Synchronization of active rotators interacting with environment
• Scaling law of transient lifetime of chimera states under dimension-augmenting perturbations
• Feedback-induced desynchronization and oscillation quenching in a population of globally coupled oscillators
• The effects of degree distributions in random networks of Type-I neurons
• Optimal control for phase locking of synchronized oscillator populations via dynamical reduction techniques
• Microscopic Cross-Correlations in the Finite-Size Kuramoto Model of Coupled Oscillators
• Theta neuron subject to delayed feedback: a prototypical model for self-sustained pulsing
• Chimera Dynamics of Generalized Kuramoto-Sakaguchi Oscillators in Two-population Networks
• Response Theory Identifies Reaction Coordinates and Explains Critical Phenomena in Noisy Interacting Systems
• Dynamics of oscillator populations globally coupled with distributed phase shifts
• Hopf Bifurcations of Twisted States in Phase Oscillators Rings with Nonpairwise Higher-Order Interactions
• Low-dimensional model for adaptive networks of spiking neurons
• The study of the dynamics of the order parameter of coupled oscillators in the Ott-Antonsen scheme for generic frequency distributions
• Spontaneous collective synchronization in the Kuramoto model with additional non-local interactions
• Irregular collective dynamics in a Kuramoto-Daido system
• Control of seizure-like dynamics in neuronal populations with excitability adaptation related to ketogenic diet
• The Sakaguchi-Kuramoto model in presence of asymmetric interactions that break phase-shift symmetry
• A new class of chimeras in locally coupled oscillators with small-amplitude, high-frequency asynchrony and large-amplitude, low-frequency synchrony
• Chaotic Chimera Attractors in a Triangular Network of Identical Oscillators
• Discordant synchronization patterns on directed networks of identical phase oscillators with attractive and repulsive couplings
• Role of Coupling Asymmetry in the Fully Disordered Kuramoto Model
• Resonances and multistability in a Josephson junction connected to a resonator
• Exponentially long transient time to synchronization of coupled chaotic circle maps in dense random networks
• Multifidelity Approximate Bayesian Computation with Sequential Monte Carlo Parameter Sampling
• An approach to normal forms of Kuramoto model with distributed delays and the effect of minimal delay
• A Two-Frequency-Two-Coupling model of coupled oscillators
• Synchronization in a System of Kuramoto Oscillators with Distributed Gaussian Noise
• The Winfree model with non-infinitesimal phase-response curve: Ott-Antonsen theory
• Spatio-temporal dynamics of Kuramoto-Sakaguchi model with time dependent connectivity
• Birth and destruction of collective oscillations in a network of two populations of coupled type 1 neurons
• Linear response theory for coupled phase oscillators with general coupling functions
• Topological phase transition in the periodically forced Kuramoto model
• Synchronization transitions in adaptive simplicial complexes with cooperative and competitive dynamics
• Avalanches impede synchronization of jammed oscillators
• Nonlinear bias of collective oscillation frequency induced by asymmetric Cauchy noise
• Low Dimensional Dynamics of Globally Coupled Complex Riccati Equations: Exact Firing-rate Equations for Spiking Neurons with Clustered Substructure
• Data-driven Selection of Coarse-Grained Models of Coupled Oscillators
• Dynamics of large oscillator populations with random interactions
• Bifurcation of the neuronal population dynamics of the modified theta model: transition to macroscopic gamma oscillation
• Möbius group actions in the solvable chimera model
• A global bifurcation organizing rhythmic activity in a coupled network
• Stability of entrainment of a continuum of coupled oscillators
• Relating high dimensional stochastic complex systems to low-dimensional intermittency
• Collective excitability in highly diluted networks of rotators
• Codimension-two Bifurcations Induce Hysteresis Behavior and Multistabilities in Delay-coupled Kuramoto Oscillators
• Correspondence between phase oscillator network and classical XY model with the same infinite-range interaction in statics
• Competitive Suppression of Synchronization and Non-Monotonic Transitions in Oscillator Communities with Distributed Time Delay
• Binary Mixtures of Locally Coupled Mobile Oscillators
• Extracting phase coupling functions between collectively oscillating networks directly from time-series data
• Mesoscopic model reduction for the collective dynamics of sparse coupled oscillator networks
• Paradoxical phase response of gamma rhythms facilitates their entrainment in heterogeneous networks
• Basins of Attraction: A Dynamical Zoo
• Collective in-plane magnetization in a 2D XY macrospin system within the framework of generalized Ott-Antonsen theory
• Parameter estimation, nonlinearity and Occam's razor
• Emergence of metastability in frustrated oscillatory networks: the key role of hierarchical modularity
• Topologically-induced suppression of explosive synchronization
• Information geometry and synchronization phase transition in Kuramoto model
• Stationary-state dynamics of interacting phase oscillators in presence of noise and stochastic resetting
• Coexistence of asynchronous and clustered dynamics in noisy inhibitory neural networks
• Understanding the surface wave characteristics using 2D particle-in-cell simulation and deep neural network
• Optimal interaction functions realizing higher-order Kuramoto dynamics with arbitrary limit-cycle oscillators
• Finite-size scaling and dynamics in a two-dimensional lattice of identical oscillators with frustrated couplings
• Uncovering low dimensional macroscopic chaotic dynamics of large finite size complex systems
• A unified analytical framework for a class of optimal control problems on networked systems
• Small and Finite Inertia in Stochastic Systems: Moment and Cumulant Formalisms
• Classification of bifurcation diagrams in coupled phase-oscillator models with asymmetric natural frequency distributions
• Kuramoto variables as eigenvalues of unitary matrices
• Chimeras with uniformly distributed heterogeneity: two coupled populations
• Using Phase Dynamics to Study Partial Synchrony: Three Examples
• Disorder-promoted stability
• Phase-locking in $k$-partite networks of delay-coupled oscillators
• Two-phase quadratic integrate-and-fire neurons: Exact low-dimensional description for ensembles of finite-voltage neurons
• The Kuramoto model on a sphere: Explaining its low-dimensional dynamics with group theory and hyperbolic geometry
• Dynamics of coupled oscillator systems in presence of a local potential
• Mean-field approximations of networks of spiking neurons with short-term synaptic plasticity
• Competing synchronization on random networks
• Mean-field approach for frequency synchronization in complex networks of two oscillator types
• Signature of glassy dynamics in dynamic modes decompositions
• Metastability of multi-population Kuramoto-Sakaguchi oscillators
• Hyperbolic chaos at blinking coupling of noisy oscillators
• Solving Sudoku using oscillatory neural networks
• Efficient moment-based approach to the simulation of infinitely many heterogeneous phase oscillators
• Four approaches for description of stochastic systems with small and finite inertia
• Characterizing correlations and synchronization in collective dynamics
• Phase transformation and synchrony for a network of coupled Izhikevich neurons
• Kinetic description of one-dimensional stochastic dynamics with small inertia
• Impact of heavy-tailed synaptic strength distributions on self-sustained activity in networks of spiking neurons
• Synchronization modes in bipartite oscillator networks
• Analytical foundation for adversarial synchronization control in oscillator networks
• Spatio-temporal patterns of active epigenetic turnover
• Dynamics in hybrid complex systems of switches and oscillators
• Phase holonomy underlies puzzling temporal patterns in Kuramoto models with two sub-populations