Structure preserving schemes for the continuum Kuramoto model: phase transitions
For researchers studying synchronization and phase transitions in oscillator networks, this work provides structure-preserving numerical tools that address high-dimensional challenges with multiple frequencies.
The authors developed numerical methods that preserve structural properties of the Kuramoto model with diffusion, enabling efficient simulation of phase transitions for identical and non-identical oscillators. The schemes accurately capture stationary states and phase transitions.
The construction of numerical schemes for the Kuramoto model is challenging due to the structural properties of the system which are essential in order to capture the correct physical behavior, like the description of stationary states and phase transitions. Additional difficulties are represented by the high dimensionality of the problem in presence of multiple frequencies. In this paper, we develop numerical methods which are capable to preserve these structural properties of the Kuramoto equation in the presence of diffusion and to solve efficiently the multiple frequencies case. The novel schemes are then used to numerically investigate the phase transitions in the case of identical and non identical oscillators.