Solitary state at the edge of synchrony in ensembles with attractive and repulsive interaction

Abstract

We discuss the desynchronization transition in networks of globally coupled identical oscillators with attractive and repulsive interactions. We show that, if attractive and repulsive groups act in antiphase or close to that, a solitary state emerges with a single repulsive oscillator split up from the others fully synchronized. With further increase of the repulsing strength, the synchronized cluster becomes fuzzy and the dynamics is given by a variety of stationary states with zero common forcing. Intriguingly, solitary states represent the natural link between coherence and incoherence. The phenomenon is described analytically for phase oscillators with sine coupling and demonstrated numerically for more general amplitude models.

5 pages, 4 figures

References in corpus (6)

• Low Dimensional Behavior of Large Systems of Globally Coupled Oscillators
• Partially integrable dynamics of hierarchical populations of coupled oscillators
• Conformists and contrarians in a Kuramoto model with identical natural frequencies
• Hierarchical Synchrony of Phase Oscillators in Modular Networks
• Multiscale Dynamics in Communities of Phase Oscillators
• Asymmetry--induced effects in coupled phase oscillator ensembles: Routes to synchronization

Cited by in corpus (49)

• Understanding the dynamics of biological and neural oscillator networks through exact mean-field reductions: a review
• The synchronized dynamics of time-varying networks
• Chimera states in brain networks: empirical neural vs. modular fractal connectivity
• Solitary states for coupled oscillators
• Enhancing power grid synchronization and stability through time delayed feedback control
• Chimera states in two populations with heterogeneous phase-lag
• Weak multiplexing in neural networks: Switching between chimera and solitary states
• Hierarchical frequency clusters in adaptive networks of phase oscillators
• Perspectives on adaptive dynamical systems
• Solitary states in adaptive nonlocal oscillator networks
• The changing notion of chimera states, a critical review
• Distance dependent competitive interactions in a frustrated network of mobile agents
• Does the brain behave like a (complex) network? I. Dynamics
• Mechanism of solitary state appearance in an ensemble of nonlocally coupled Lozi maps
• Perspective on attractive-repulsive interactions in dynamical networks: progress and future
• Low-Dimensional Dynamics for Higher Order Harmonic Globally Coupled Phase Oscillator Ensemble
• Effect of repulsive links on frustration in attractively coupled networks
• Solitary States and Partial Synchrony in Oscillatory Ensembles with Attractive and Repulsive Interactions
• Collective dynamics in two populations of noisy oscillators with asymmetric interactions
• Unbalanced clustering and solitary states in coupled excitable systems
• Role of solitary states in forming spatiotemporal patterns in a 2D lattice of van der Pol oscillators
• Solitary states in multiplex neural networks: onset and vulnerability
• Dynamics of Kuramoto oscillators with time-delayed positive and negative couplings
• Generalized splay states in phase oscillator networks
• On the analysis of a time varying noise-modulated heterogeneous coupled network of Chialvo neurons under the influence of electromagnetic flux
• Repulsively Coupled Kuramoto-Sakaguchi Phase Oscillators Ensemble Subject to Common Noise
• Chimera states and synchronization in magnetically driven SQUID metamaterials
• Long-range interaction induced collective dynamical behaviors
• Delay engineered solitary states in complex networks
• Dynamics of the Kuramoto-Sakaguchi Oscillator Network with Asymmetric Order Parameter
• Chimera at the phase-flip transition of an ensemble of identical nonlinear oscillators
• Transition from chimera/solitary states to traveling waves
• Synchronization transitions in Kuramoto networks with higher-mode interaction
• Stability of rotatory solitary states in Kuramoto networks with inertia
• Machine Learning assisted Chimera and Solitary states in Networks
• Solitary states in the mean-field limit
• Adversarial decision strategies in multiple network phased oscillators: the Blue-Green-Red Kuramoto-Sakaguchi model
• Solitary routes to chimera states
• Mixed-Mode Chimera states in Pendula Networks
• Energy balance and energy correction in dynamics of classical spin systems
• Solitary states in complex networks: impact of topology
• Symmetry broken states in an ensemble of globally coupled pendulums
• Dynamics of oscillator populations globally coupled with distributed phase shifts
• A Two-Frequency-Two-Coupling model of coupled oscillators
• Moderate Higher-Order Interactions Enhance Stability While Preserving Basin Structure
• Resonant Solitary States in Complex Networks
• Traveling phase waves in asymmetric networks of noisy chaotic attractors
• Dynamics of a 2D lattice of van der Pol oscillators with nonlinear repulsive coupling
• Using Phase Dynamics to Study Partial Synchrony: Three Examples