Hopf Bifurcations of Twisted States in Phase Oscillators Rings with Nonpairwise Higher-Order Interactions

Abstract

Synchronization is an essential collective phenomenon in networks of interacting oscillators. Twisted states are rotating wave solutions in ring networks where the oscillator phases wrap around the circle in a linear fashion. Here, we analyze Hopf bifurcations of twisted states in ring networks of phase oscillators with nonpairwise higher-order interactions. Hopf bifurcations give rise to quasiperiodic solutions that move along the oscillator ring at nontrivial speed. Because of the higher-order interactions, these emerging solutions may be stable. Using the Ott--Antonsen approach, we continue the emergent solution branches which approach anti-phase type solutions (where oscillators form two clusters whose phase is $\pi$ apart) as well as twisted states with a different winding number.

arXiv comment24 pages, 8 figures

References in corpus (18)

• Networks beyond pairwise interactions: structure and dynamics
• Chimera States for Coupled Oscillators
• The Kuramoto model in complex networks
• Low Dimensional Behavior of Large Systems of Globally Coupled Oscillators
• What are higher-order networks?
• Higher-order interactions in complex networks of phase oscillators promote abrupt synchronization switching
• Abrupt Desynchronization and Extensive Multistability in Globally Coupled Oscillator Simplices
• Phase reduction approach to synchronization of nonlinear oscillators
• Understanding the dynamics of biological and neural oscillator networks through exact mean-field reductions: a review
• Chaos in generically coupled phase oscillator networks with nonpairwise interactions
• Controlling Chimeras
• Phase reduction beyond the first order: the case of the mean-field complex Ginzburg-Landau equation
• Hopf normal form with $S_N$ symmetry and reduction to systems of nonlinearly coupled phase oscillators
• Stability of twisted states in the Kuramoto model on Cayley and random graphs
• Mathematical framework for breathing chimera states
• Phase Oscillator Networks with Nonlocal Higher-Order Interactions: Twisted States, Stability and Bifurcations
• Higher-Order Network Interactions through Phase Reduction for Oscillators with Phase-Dependent Amplitude
• Periodic orbits in the Ott-Antonsen manifold

Cited by in corpus (2)

• Deeper but smaller: Higher-order interactions increase linear stability but shrink basins
• Collective dynamics on higher-order networks