Solitary States and Partial Synchrony in Oscillatory Ensembles with Attractive and Repulsive Interactions

Abstract

We numerically and analytically analyze transitions between different synchronous states in a network of globally coupled phase oscillators with attractive and repulsive interactions. The elements within the attractive or repulsive group are identical, but natural frequencies of the groups differ. In addition to a synchronous two-cluster state, the system exhibits a solitary state, when a single oscillator leaves the cluster of repulsive elements, as well as partially synchronous quasiperiodic dynamics. We demonstrate how the transitions between these states occur when the repulsion starts to prevail over attraction.

References in corpus (26)

• Low Dimensional Behavior of Large Systems of Globally Coupled Oscillators
• Chimera States in Mechanical Oscillator Networks
• Solvable model for chimera states of coupled oscillators
• Coexistence of Coherence and Incoherence in Nonlocally Coupled Phase Oscillators
• Long Time Evolution of Phase Oscillator Systems
• Dynamic Balance of Excitation and Inhibition in Human and Monkey Neocortex
• Partially integrable dynamics of hierarchical populations of coupled oscillators
• Thermodynamic limit of the first-order phase transition in the Kuramoto model
• Synchronization of two interacting populations of oscillators
• Chimera-like states in an ensemble of globally coupled oscillators
• Phase oscillators with global sinusoidal coupling evolve by Mobius group action
• Conformists and contrarians in a Kuramoto model with identical natural frequencies
• Chimera states in brain networks: empirical neural vs. modular fractal connectivity
• Synchronization in networks of networks: the onset of coherent collective behavior in systems of interacting populations of heterogeneous oscillators
• Solitary state at the edge of synchrony in ensembles with attractive and repulsive interaction
• Solitary states for coupled oscillators
• Stationary and Traveling Wave States of the Kuramoto Model with an Arbitrary Distribution of Frequencies and Coupling Strengths
• Weak multiplexing in neural networks: Switching between chimera and solitary states
• Interplay of coupling and common noise at the transition to synchrony in oscillator populations
• Mechanism of solitary state appearance in an ensemble of nonlocally coupled Lozi maps
• Multiscale Dynamics in Communities of Phase Oscillators
• A minimal model of partial synchrony
• Synchronization of oscillators in a Kuramoto-type model with generic coupling
• Chimera states and synchronization in magnetically driven SQUID metamaterials
• Long-range interaction induced collective dynamical behaviors
• Dynamics of the Kuramoto-Sakaguchi Oscillator Network with Asymmetric Order Parameter

Cited by in corpus (12)

• Solitary states in adaptive nonlocal oscillator networks
• Perspective on attractive-repulsive interactions in dynamical networks: progress and future
• Unbalanced clustering and solitary states in coupled excitable systems
• Generalized splay states in phase oscillator networks
• Cyclops states in repulsive Kuramoto networks: the role of higher-order coupling
• Aging transition under discrete time-dependent coupling: Restoring rhythmicity from aging
• Stability of rotatory solitary states in Kuramoto networks with inertia
• Synchronization transitions in Kuramoto networks with higher-mode interaction
• Machine Learning assisted Chimera and Solitary states in Networks
• A Two-Frequency-Two-Coupling model of coupled oscillators
• Using Phase Dynamics to Study Partial Synchrony: Three Examples
• Effect of atom-oscillator interaction on the aging transition in coupled oscillators