Bifurcations in the Kuramoto model with external forcing and higher-order interactions
arXiv:2409.08736 · doi:10.1063/5.0239011
Abstract
Synchronization is an important phenomenon in a wide variety of systems comprising interacting oscillatory units, whether natural (like neurons, biochemical reactions, cardiac cells) or artificial (like metronomes, power grids, Josephson junctions). The Kuramoto model provides a simple description of these systems and has been useful in their mathematical exploration. Here we investigate this model combining two common features that have been observed in many systems: external periodic forcing and higher-order interactions among the elements. We show that the combination of these ingredients leads to a very rich bifurcation scenario that produces 11 different asymptotic states of the system, with competition between forced and spontaneous synchronization. We found, in particular, that saddle-node, Hopf and homoclinic manifolds are duplicated in regions of parameter space where the unforced system displays bi-stability.
Updated version; 18 pages; 5 figures
References in corpus (33)
- Synchronization in complex networks
- Networks beyond pairwise interactions: structure and dynamics
- Higher-order organization of complex networks
- The Kuramoto model in complex networks
- Low Dimensional Behavior of Large Systems of Globally Coupled Oscillators
- Simplicial models of social contagion
- Explosive Synchronization Transitions in Scale-free Networks
- Clique topology reveals intrinsic geometric structure in neural correlations
- Higher-order interactions in complex networks of phase oscillators promote abrupt synchronization switching
- Abrupt Desynchronization and Extensive Multistability in Globally Coupled Oscillator Simplices
- Social contagion models on hypergraphs
- Stability diagram for the forced Kuramoto model
- Cluster Explosive Synchronization in Complex Networks
- Chaos in generically coupled phase oscillator networks with nonpairwise interactions
- Multistable attractors in a network of phase oscillators with three-body interaction
- Phase reduction beyond the first order: the case of the mean-field complex Ginzburg-Landau equation
- Simplicial SIS model in scale-free uniform hypergraph
- Hopf normal form with symmetry and reduction to systems of nonlinearly coupled phase oscillators
- Fitness for Synchronization of Network Motifs
- Synchronization and spatial patterns in forced swarmalators
- D-dimensional oscillators in simplicial structures: odd and even dimensions display different synchronization scenarios
- Global synchronization of partially forced Kuramoto oscillators on Networks
- Higher-order interactions induce anomalous transitions to synchrony
- Phase chimera states on non-local hyperrings
- Ott-Antonsen ansatz for the D-dimensional Kuramoto model: a constructive approach
- Modular structure in C. elegans neural network and its response to external localized stimuli
- Optimal global synchronization of partially forced Kuramoto oscillators
- Kuramoto model with uniformly spaced frequencies:Finite-N asymptotics of the locking threshold
- Cooperation and Competition in Synchronous Open Quantum Systems
- Driven synchronization in random networks of oscillators
- Synchronization transitions on connectome graphs with external force
- Exploring the phase diagrams of multidimensional Kuramoto models
- Third order interactions shift the critical coupling in multidimensional Kuramoto models