Related papers: Synchronization of Phase-coupled Oscillators with …
Brain networks typically exhibit characteristic synchronization patterns where several synchronized clusters coexist. On the other hand, neurological disorders are considered to be related to pathological synchronization such as excessive…
Network couplings of oscillatory large-scale systems, such as the brain, have a space-time structure composed of connection strengths and signal transmission delays. We provide a theoretical framework, which allows treating the spatial…
We explore identical R\"ossler systems organized into two equally-sized groups, among which differing positive and negative in- and out-coupling strengths are allowed. Patterns of distinctly synchronized phase dynamics are observed, which…
We introduce a novel coupling scheme for maximizing the synchronization of Kuramoto oscillator networks under a fixed coupling budget. We show that by scaling the interaction strength between oscillators according to their frequency…
We introduce a system of pulse coupled oscillators that can change both their phases and frequencies; and prove that when there is a separation of time scales between phase and frequency adjustment the system converges to exact synchrony on…
Partial integrability in phase-oscillator dynamics is typically examined for identically connected oscillators or groups thereof. Yet, the precise connectivity conditions that ensure conserved quantities on general networks remain unclear.…
The Kuramoto model for an ensemble of coupled oscillators provides a paradigmatic example of non-equilibrium transitions between an incoherent and a synchronized state. Here we analyze populations of almost identical oscillators in…
A two-time scale asymptotic method has been introduced to analyze the multimodal mean-field Kuramoto-Sakaguchi model of oscillator synchronization in the high-frequency limit. The method allows to uncouple the probability density in…
The Kuramoto model serves as a paradigm for describing spontaneous synchronization in a system of classical interacting rotors. In this study, we extend this model to the quantum domain by coupling quantum interacting rotors to external…
We study Kuramoto oscillators, driven by one pacemaker, on $d$-dimensional regular topologies with nearest neighbor interactions. We derive the analytical expressions for the common frequency in the case of phase-locked motion and for the…
We present an improved and more accurate numerical scheme for a generalization of the Kuramoto model of coupled phase oscillators to the three-dimensional space. The present numerical scheme relies crucially on our observation that the…
The Kuramoto model is a versatile mathematical framework that explains phenomena resulting from interactions among phase oscillators. It finds applications in various scientific and engineering domains. In this study, we focused on a…
The Frimmer-Novotny model to simulate two-level systems by coupled oscillators is extended by incorporating a constant time delay in the coupling. The effects of the introduced delay on system dynamics and two-level modeling are then…
Linear stability of synchronized states in networks of delay-coupled oscillators depends on the type of interaction, the network and oscillator properties. For inert oscillator response, found ubiquitously from biology to engineering,…
We study the interplay between non-Hermitian dynamics and phase synchronization in a system of $\mathcal{N}$ bosonic modes coupled to an auxiliary mode. The linearity of the evolution in such a system allows for the derivation of fully…
Networks of coupled phase oscillators play an important role in the analysis of emergent collective phenomena. In this article, we introduce generalized $m$-splay states constituting a special subclass of phase-locked states with vanishing…
The Kuramoto model has become a paradigm to describe the dynamics of nonlinear oscillator under the influence of external perturbations, both deterministic and stochastic. It is based on the idea to describe the oscillator dynamics by a…
In this paper, by extending the concept of Kuramoto oscillator to the left-invariant flow on general Lie group, we investigate the generalized phase synchronization on networks. The analyses and simulations of some typical dynamical systems…
We analyze star-type networks of phase oscillators by virtue of two methods. For identical oscillators we adopt the Watanabe-Strogatz approach, that gives full an- alytical description of states, rotating with constant frequency. For…
We investigate "chimera" states in a ring of identical phase oscillators coupled in a time-delayed and spatially non-local fashion. We find novel "clustered chimera" states that have spatially distributed phase coherence separated by…