Collective dynamics and bifurcations in symmetric networks of phase oscillators. I

DOI10.1007/s10958-020-04959-yzbMath1454.34002OpenAlexW3049460516MaRDI QIDQ2202851

O. A. Burylko

Publication date: 30 September 2020

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-020-04959-y

zbMATH Keywords

synchronybifurcationcoupled oscillatorsKuramoto model

Mathematics Subject Classification ID

Symmetries, invariants of ordinary differential equations (34C14) Bifurcation theory for ordinary differential equations (34C23) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Research exposition (monographs, survey articles) pertaining to ordinary differential equations (34-02) Biological rhythms and synchronization (92B25) Synchronization of solutions to ordinary differential equations (34D06)

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Cites Work

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• Mathematical frameworks for oscillatory network dynamics in neuroscience
• Bifurcations in phase oscillator networks with a central element
• Synchronization in complex networks of phase oscillators: a survey
• The Kuramoto model in complex networks
• Dynamics of heterogeneous oscillator ensembles in terms of collective variables
• Desynchronization transitions in nonlinearly coupled phase oscillators
• Is there switching for replicator dynamics and bimatrix games?
• Chemical oscillations, waves, and turbulence
• Three coupled oscillators: Mode-locking, global bifurcations and toroidal chaos
• The dynamics of chimera states in heterogeneous Kuramoto networks
• Specific locking in populations dynamics: symmetry analysis for coupled heteroclinic cycles
• Symmetric bifurcation analysis of synchronous states of time-delayed coupled phase-locked loop oscillators
• Synchronization. From simple to complex
• Time-reversal symmetry in dynamical systems: a survey
• Self-organized partially synchronous dynamics in populations of nonlinearly coupled oscillators
• Reversible systems
• Synchronization in a neural network of phase oscillators with the central element
• Constants of motion for superconducting Josephson arrays
• Weakly connected neural networks
• The dynamics of \(n\) weakly coupled identical oscillators
• From Kuramoto to Crawford: Exploring the onset of synchronization in population of coupled oscillators
• Phase locking in chains of multiple-coupled oscillators
• The synchronization of chaotic systems
• Reversibility vs. synchronization in oscillator lattices
• Gaussian noise and the two-network frustrated Kuramoto model
• Heteroclinic networks in coupled cell systems
• Synchronization of globally coupled phase oscillators: singularities and scaling for general couplings
• Statistical macrodynamics of large dynamical systems. Case of a phase transition in oscillator communities
• Onset of cooperative entrainment in limit-cycle oscillators with uniform all-to-all interactions: Bifurcation of the order function
• Cluster synchronization in coupled systems with hub structure
• Stability of an \([N/2\)-dimensional invariant torus in the Kuramoto model at small coupling]
• Complex networks: structure and dynamics
• Bifurcation to heteroclinic cycles and sensitivity in three and four coupled phase oscillators
• Phase compactons
• Multiple pulse interactions and averaging in systems of coupled neural oscillators
• Multistability of phase-locking and topological winding numbers in locally coupled Kuramoto models on single-loop networks
• Chaotic weak chimeras and their persistence in coupled populations of phase oscillators
• Weak chimeras in minimal networks of coupled phase oscillators
• Plasticity and learning in a network of coupled phase oscillators
• Frequency Plateaus in a Chain of Weakly Coupled Oscillators, I.
• Discrete Time Kuramoto Models with Delay
• Three identical oscillators with symmetric coupling
• Synchronization in large directed networks of coupled phase oscillators
• PHASE CHAOS IN THE DISCRETE KURAMOTO MODEL
• Dynamics on Networks of Cluster States for Globally Coupled Phase Oscillators
• Controlled perturbation-induced switching in pulse-coupled oscillator networks
• Chaotic streamlines in the ABC flows
• Integrability of a globally coupled oscillator array
• Existence and stability of chimera states in a minimal system of phase oscillators
• Clustering versus non-clustering phase synchronizations
• Synchronization of chaotic systems
• Star-type oscillatory networks with generic Kuramoto-type coupling: A model for “Japanese drums synchrony”
• Chaos in generically coupled phase oscillator networks with nonpairwise interactions
• Coexistence of Hamiltonian-Like and Dissipative Dynamics in Rings of Coupled Phase Oscillators with Skew-Symmetric Coupling
• Long time evolution of phase oscillator systems
• Exploring complex networks
• The Kuramoto Model on Oriented and Signed Graphs
• CHIMERA STATES IN A RING OF NONLOCALLY COUPLED OSCILLATORS
• Quantifying Noisy Attractors: From Heteroclinic to Excitable Networks
• Averaging methods in nonlinear dynamical systems
• The geometry of biological time.

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