Semidefinite Programming Certificates for Synchronization of Kuramoto Oscillators on Arcs
Summary
arXiv:2606.03591v1 Announce Type: cross Abstract: A class of Kuramoto models with a general coupling function that can be expressed in terms of a finite number of harmonics, each comprising sinusoidal terms, is studied. We propose a novel approach for certifying local phase synchronization in this class for all initial conditions lying on an arc. The trace parametrization property and Gram matrix representation of a trigonometric polynomial are utilized along with Putinar's Positivstellensatz to obtain semidefinite programming certificates for the stability of the phase-difference system, which in turn implies synchronization of the original system.
Why It Matters
This Advanced Manufacturing development raises the bar for precision and smart-factory capability in the region. For Singapore, it is a signal worth tracking: it shapes who supplies, who scales, and who sets the standard over the next five years.
Key Facts
- SectorAdvanced Manufacturing
- MarketSingapore
- ImpactLow (42/100)
- SignalResearch