Related papers: A unified framework for Simplicial Kuramoto models
In future power systems, electrical storage will be the key technology for balancing feed-in fluctuations. With increasing share of renewables and reduction of system inertia, the focus of research expands towards short-term grid dynamics…
We study the dynamics of a generalized version of the famous Kuramoto-Sakaguchi coupled oscillator model. In the classic version of this system, all oscillators are governed by the same ODE, which depends on the order parameter of the…
The Kuramoto model, originally proposed to model the dynamics of many interacting oscillators, has been used and generalized for a wide range of applications involving the collective behavior of large heterogeneous groups of dynamical units…
Coupled oscillator networks show a complex interrelations between topological characteristics of the network and the nonlinear stability of single nodes with respect to large but realistic perturbations. We extend previous results on these…
Networks of phase oscillators can serve as dense associative memories if they incorporate higher-order coupling beyond the classical Kuramoto model's pairwise interactions. Here we introduce a generalized Kuramoto model with combined…
Synchronization of coupled oscillators is often described using the Kuramoto model. Here we study a generalization of the Kuramoto model where oscillators communicate with each other through an external medium. This generalized model…
We investigate hysteresis in a generalized Kuramoto model with identical oscillators, focusing on coupling strength inhomogeneity, which results in oscillators being coupled to others with varying strength, and a simplified, more realistic…
Many natural and human-made complex systems feature group interactions that adapt over time in response to their dynamic states. However, most of the existing adaptive network models fall short of capturing these group dynamics, as they…
Synchronization underlies phenomena including memory and perception in the brain, coordinated motion of animal flocks, and stability of the power grid. These synchronization phenomena are often modeled through networks of phase-coupled…
Simplicial complexes constitute the underlying topology of interacting complex systems including among the others brain and social interaction networks. They are generalized network structures that allow to go beyond the framework of…
In this paper we address two questions about the synchronization of coupled oscillators in the Kuramoto model with all-to-all coupling. In the first part we use some classical results in convex geometry to prove bounds on the size of the…
We study systems of Kuramoto oscillators, driven by one pacemaker, on $d$-dimensional regular topologies like linear chains, rings, hypercubic lattices and Cayley-trees. For the special cases of next-neighbor and infinite-range…
Complex networks often possess communities defined based on network connectivity. When dynamics undergo in a network, one can also consider dynamical communities; i.e., a group of nodes displaying a similar dynamical process. We have…
We propose a modification of the Kuramoto model to account for the effective change in the coupling constant among the oscillators, as suggested by some experiments on Josephson junction, laser arrays and mechanical systems, where the…
Nature is pervaded with oscillatory dynamics. In networks of coupled oscillators patterns can arise when the system synchronizes to an external input. Hence, these networks provide processing and memory of input. We present a universal…
Higher-order interactions fundamentally shape collective dynamics in oscillator networks. The topological Kuramoto model captures these effects by extending synchronization models to include interactions between cells of arbitrary dimension…
Due to its description of a synchronization between oscillators, the Kuramoto model is an ideal choice for a synchronisation algorithm in networked systems. This requires to achieve not only a frequency synchronization but also a phase…
Using a recently introduced linear reformulation of the Kuramoto model of self-synchronizing oscillator systems (arXiv:0704.1166), we study a new class of analytically solvable oscillator systems defined by a particular coupling scheme. We…
In this review, we discuss critical dynamics of simple nonequilibrium models on large connectomes, obtained by diffusion MRI, representing the white matter of the human brain. In the first chapter, we overview graph theoretical and…
Using a survey of wristwatch synchronization from a randomly selected group of independent volunteers, one can model the system as a Kuramoto-type coupled oscillator network. Based on the phase data, both the order parameter and an…