Collective dynamics in two populations of noisy oscillators with asymmetric interactions

Abstract

We study two intertwined globally coupled networks of noisy Kuramoto phase oscillators that have the same natural frequency, but differ in their perception of the mean field and their contribution to it. Such a give-and-take mechanism is given by asymmetric in- and out-coupling strengths which can be both positive and negative. We uncover in this minimal network of networks intriguing patterns of discordance, where the ensemble splits into two clusters separated by a constant phase lag. If it differs from $\pi$, then traveling wave solutions emerge. We observe a second route to traveling waves via traditional one-cluster states. Bistability is found between the various collective states. Analytical results and bifurcation diagrams are derived with a reduced system.

8 pages, 5 figures, published in Phys. Rev. E

References in corpus (5)

• The structure and dynamics of multilayer networks
• Explosive Synchronization Transitions in Scale-free Networks
• Thermodynamic limit of the first-order phase transition in the Kuramoto model
• Synchronization of oscillators in a Kuramoto-type model with generic coupling
• Cooperative behavior between oscillatory and excitable units: the peculiar role of positive coupling-frequency correlations

Cited by in corpus (5)

• New type of chimera and mutual synchronization of spatiotemporal structures in two coupled ensembles of nonlocally interacting chaotic maps
• Nonreciprocal Synchronization of Active Quantum Spins
• Circular cumulant reductions for macroscopic dynamics of oscillator populations with non-Gaussian noise
• Discordant synchronization patterns on directed networks of identical phase oscillators with attractive and repulsive couplings
• Gaussian theory for spatially distributed self-propelled particles