Stability and bifurcation of collective dynamics in phase oscillator populations with general coupling

Effect of adaptation functions and multilayer topology on synchronization

This study investigates the synchronization of globally coupled Kuramoto oscillators in monolayer and multilayer configurations. The interactions are taken to be pairwise, whose strength adapts with the instantaneous synchronization order parameter. The route to synchronization is analytically investigated using the Ott-Antonsen ansatz for two broad classes of adaptation functions that capture a wide range of transition scenarios. The formulation is subsequently extended to adaptively coupled multilayer configurations, using which a wider range of transition scenarios is uncovered for a bilayer model with cross-adaptive interlayer interactions.

Partial locking in phase-oscillator populations with heterogenous coupling

We consider a variant of the mean-field model of coupled phase oscillators with uniform distribution of natural frequencies. By establishing correlations between the quenched disorder of intrinsic frequencies and coupling strength with both in- and out-coupling heterogeneities, we reveal a generic criterion for the onset of partial locking that takes place in a domain with the coexistence of phase-locked oscillators and drifters. The critical points manifesting the instability of the stationary states are obtained analytically. In particular, the bifurcation mechanism of the equilibrium states is uncovered by the use of frequency-dependent version of the Ott-Antonsen reduction consistently with the analysis based on the self-consistent approach. We demonstrate that both the manner of coupling heterogeneity and correlation exponent have influence on the emergent patterns of partial locking. Our research could find applicability in better understanding the phase transitions and related collective phenomena involving synchronization control in networked systems.

Collective dynamics of phase oscillator populations with three-body interactions

Many-body interactions between dynamical agents have caught particular attention in recent works that found wide applications in physics, neuroscience, and sociology. In this paper we investigate such higher order (nonadditive) interactions on collective dynamics in a system of globally coupled heterogeneous phase oscillators. We show that the three-body interactions encoded microscopically in nonlinear couplings give rise to added dynamic phenomena occurring beyond the pairwise interactions. The system in general displays an abrupt desynchronization transition characterized by irreversible explosive synchronization via an infinite hysteresis loop. More importantly, we give a mathematical argument that such an abrupt dynamic pattern is a universally expected effect. Furthermore, the origin of this abrupt transition is uncovered by performing a rigorous stability analysis of the equilibrium states, as well as by providing a detailed description of the spectrum structure of linearization around the steady states. Our work reveals a self-organized phenomenon that is responsible for the rapid switching to synchronization in diverse complex systems exhibiting critical transitions with nonpairwise interactions.