Spatiotemporal Dynamics of the Kuramoto-Sakaguchi Model with Time-dependent Connectivity

We study the dynamics of the Kuramoto-Sakaguchi synchronization model with interaction involving a time-dependent coupling range. Statistical quantities measuring coherence and phase discontinuity are used to distinguish between various collective states and we plot their phase diagrams in the planes defined by various parameters of the system. A sinusoidal variation of the coupling radius leads to a hysteretic response of the system depending on the strength of coupling. This indicates the existence of an intrinsic time-scale in the system competing with the time period of the coupling range, which is verified from the mean field Ott-Antonsen analysis as well as direct simulation. The findings may be applied to diverse situations, e.g., dynamics involving plastic neural connections or human beings gathered by some common time-dependent source of excitation; and hence can open new vistas of diverse applicability of the decades-old Kuramoto model while the latter may then widen its scope to explain natural and social phenomena arising out of collective dynamics.
Main Publication: Phys. Rev. E 94, 022213 (2016)