Star-type oscillatory networks with generic Kuramoto-type coupling: a model for "Japanese drums synchrony"

Abstract

We analyze star-type networks of phase oscillators by virtue of two methods. For identical oscillators we adopt the Watanabe-Strogatz approach, that gives full an- alytical description of states, rotating with constant frequency. For nonidentical oscillators, such states can be obtained by virtue of the self-consistent approach in a parametric form. In this case stability analysis cannot be performed, however with the help of direct numerical simulations we show which solutions are stable and which not. We consider this system as a model for a drum orchestra, where we assume that the drummers follow the signal of the leader without listening to each other and the coupling parameters are determined by a geometrical organization of the orchestra.

30 pages, 11 figures

References in corpus (2)

• Low Dimensional Behavior of Large Systems of Globally Coupled Oscillators
• Synchronization of oscillators in a Kuramoto-type model with generic coupling

Cited by in corpus (8)

• Hyperbolic Geometry of Kuramoto Oscillator Networks
• Dynamics of phase oscillators in the Kuramoto model with generalized frequency-weighted coupling
• Dynamics of weakly inhomogeneous oscillator populations: Perturbation theory on top of Watanabe-Strogatz integrability
• Order parameter analysis of synchronization transitions on star networks
• Dynamics of the Kuramoto-Sakaguchi Oscillator Network with Asymmetric Order Parameter
• Stability of Remote Synchronization in Star Networks of Kuramoto Oscillators
• Dynamics of oscillator populations globally coupled with distributed phase shifts
• Chimera states through invariant manifold theory