Identical phase oscillators with global sinusoidal coupling evolve by Möbius group action

DOI10.1063/1.3247089zbMath1311.34082arXiv0904.1680OpenAlexW2009885820WikidataQ33348439 ScholiaQ33348439MaRDI QIDQ5250377

Seth A. Marvel, Renato E. Mirollo, Steven H. Strogatz

Publication date: 19 May 2015

Published in: Chaos: An Interdisciplinary Journal of Nonlinear Science (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0904.1680

Mathematics Subject Classification ID

Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45)

Related Items

On the double sphere model of synchronization, Magnetization dynamics and geometry: coupled Möbius transformations, Complexity reduction in the 3D Kuramoto model, The dynamics of chimera states in heterogeneous Kuramoto networks, Circular cumulant reductions for macroscopic dynamics of Kuramoto ensemble with multiplicative intrinsic noise, Explosive synchronization in bipartite networks, Phase-lock effect for equations modeling resistively shunted Josephson junctions and for their perturbations, Consensus and balancing on the three-sphere, Higher-dimensional generalizations of the Watanabe–Strogatz transform for vector models of synchronization, The asymptotic behavior of the order parameter for the infinite-N Kuramoto model, Collective motions of globally coupled oscillators and some probability distributions on circle, Chimera dynamics of generalized Kuramoto–Sakaguchi oscillators in two-population networks, Classification of attractors for systems of identical coupled Kuramoto oscillators, Model reduction for networks of coupled oscillators, Dynamics of globally coupled oscillators: Progress and perspectives, Star-type oscillatory networks with generic Kuramoto-type coupling: A model for “Japanese drums synchrony”, Characterizing complex networks through statistics of Möbius transformations, Multisoliton complex systems with explicit superpotential interactions, Volcano transition in a system of generalized Kuramoto oscillators with random frustrated interactions, Conformists and contrarians on spheres, Ott-Antonsen attractiveness for parameter-dependent oscillatory systems, The WS transform for the Kuramoto model with distributed amplitudes, phase lag and time delay, Hyperbolic geometry of Kuramoto oscillator networks, Understanding the dynamics of biological and neural oscillator networks through exact mean-field reductions: a review, Interplay of the mechanisms of synchronization by common noise and global coupling for a general class of limit-cycle oscillators, Bifurcations in phase oscillator networks with a central element, Competition for synchronization in a phase oscillator system, Complete Classification of the Macroscopic Behavior of a Heterogeneous Network of Theta Neurons, Kantorovich–Rubinstein–Wasserstein distance between overlapping attractor and repeller, Dynamics of the Kuramoto-Sakaguchi oscillator network with asymmetric order parameter, Networks of theta neurons with time-varying excitability: macroscopic chaos, multistability, and final-state uncertainty, Complex macroscopic behavior in systems of phase oscillators with adaptive coupling, Collective phase dynamics of globally coupled oscillators: noise-induced anti-phase synchronization, Fronts and bumps in spatially extended Kuramoto networks, Abnormal hybrid phase transition in the passively competing Kuramoto model, Repulsively coupled Kuramoto-Sakaguchi phase oscillators ensemble subject to common noise, Collective dynamics from stochastic thermodynamics, Heteroclinic and homoclinic structures in the system of four identical globally coupled phase oscillators with nonpairwise interactions, On synchronization in Kuramoto models on spheres, Modelling mean fields in networks of coupled oscillators, Uncovering low dimensional macroscopic chaotic dynamics of large finite size complex systems, Finite-size effects in a stochastic Kuramoto model, Computing the Douady-Earle extension using Kuramoto oscillators, Dynamics of heterogeneous oscillator ensembles in terms of collective variables, Analytical properties of horizontal visibility graphs in the Feigenbaum scenario, Chaos in Kuramoto oscillator networks, Low-dimensional dynamics in non-Abelian Kuramoto model on the 3-sphere, The dynamics of networks of identical theta neurons, Topaj-Pikovsky involution in the Hamiltonian lattice of locally coupled oscillators, Solvable model of the collective motion of heterogeneous particles interacting on a sphere, Control of collective network chaos, Systems of matrix Riccati equations, linear fractional transformations, partial integrability and synchronization, Mathematical framework for breathing Chimera states, Data-driven stochastic modeling of coarse-grained dynamics with finite-size effects using Langevin regression, Collective in-plane magnetization in a two-dimensional XY macrospin system within the framework of generalized Ott–Antonsen theory, Solitary states and partial synchrony in oscillatory ensembles with attractive and repulsive interactions, Chimera states through invariant manifold theory, Phase synchronization between collective rhythms of globally coupled oscillator groups: Noiseless nonidentical case, Competing synchronization on random networks, Dynamics of coupled oscillators with convex interaction potential, Generalized splay states in phase oscillator networks, Comment on “Long time evolution of phase oscillator systems” [Chaos 19, 023117 (2009)], Center manifold reduction for large populations of globally coupled phase oscillators, Constants of motion for the finite-dimensional Lohe type models with frustration and applications to emergent dynamics, On reversibility of macroscopic and microscopic dynamics in the Kuramoto model

Cites Work