Large-scale spatiotemporal patterns in a ring of nonlocally coupled oscillators with a repulsive coupling

Metastability of multi-population Kuramoto-Sakaguchi oscillators

An Ott-Antonsen reduced M-population of Kuramoto-Sakaguchi oscillators is investigated, focusing on the influence of the phase-lag parameter α on the collective dynamics. For oscillator populations coupled on a ring, we obtained a wide variety of spatiotemporal patterns, including coherent states, traveling waves, partially synchronized states, modulated states, and incoherent states. Back-and-forth transitions between these states are found, which suggest metastability. Linear stability analysis reveals the stable regions of coherent states with different winding numbers q. Within certain α ranges, the system settles into stable traveling wave solutions despite the coherent states also being linearly stable. For around α≈0.46π, the system displays the most frequent metastable transitions between coherent states and partially synchronized states, while for α closer to π/2, metastable transitions arise between partially synchronized states and modulated states. This model captures metastable dynamics akin to brain activity, offering insights into the synchronization of brain networks.

Deterministic correlations enhance synchronization in oscillator populations with heterogeneous coupling

Synchronization is a critical phenomenon that displays a pivotal role in a wealth of dynamical processes ranging from natural to artificial systems. Here, we untangle the synchronization optimization in a system of globally coupled phase oscillators incorporating heterogeneous interactions encoded by the deterministic-random coupling. We uncover that, within the given restriction, the added deterministic correlations can profoundly enhance the synchronizability in comparison with the uncorrelated scenario. The critical points manifesting the onset of synchronization and desynchronization transitions, as well as the level of phase coherence, are significantly shaped by the increment of deterministic correlations. In particular, we provide an analytical treatment to properly ground the mechanism underlying synchronization enhancement and substantiate that the analytical predictions are in fair agreement with the numerical simulations. This study is a step forward in highlighting the importance of heterogeneous coupling among dynamical agents, which provides insights for control strategies of synchronization in complex systems.

Effect of mobility on collective phase dynamics of nonlocally coupled oscillators with a phase lag

Nonlocally coupled oscillators with a phase lag self-organize into various patterns, such as global synchronization, the twisted state, and the chimera state. In this paper, we consider nonlocally coupled oscillators that move on a ring by randomly exchanging their positions with the neighbors and investigate the combined effects of phase lag and mobility on the collective phase dynamics. Spanning the whole range of phase lag and mobility, we show that mobility promotes synchronization for an attractive coupling, whereas it destroys coherence for a repulsive coupling. The transition behaviors are discussed in terms of the timescales of synchronization and diffusion of the oscillators. We also find a novel spatiotemporal pattern at the border between coherent and incoherent states.