Related papers: Explosive higher-order Kuramoto dynamics on simpli…
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…
Understanding how the interplay between higher-order and multilayer structures of interconnections influences the synchronization behaviors of dynamical systems is a feasible problem of interest, with possible application in essential…
By means of numerical analysis conducted with the aid of the computer, the collective synchronization of coupled phase oscillators in the Kuramoto model in the connected regime of random networks of various sizes is studied. The oscillators…
The Kuramoto model describes a system of globally coupled phase-only oscillators with distributed natural frequencies. The model in the steady state exhibits a phase transition as a function of the coupling strength, between a low-coupling…
We study synchronization in a Kuramoto model of globally coupled phase oscillators with a bi-harmonic coupling function, in the thermodynamic limit of large populations. We develop a method for an analytic solution of self-consistent…
We study the synchronization of a generalized Kuramoto system in which the coupling weights are determined by the phase differences between oscillators. We employ the fast-learning regime in a Hebbian-like plasticity rule so that the…
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…
Finite-size systems of Kuramoto model display intricate dynamics, especially in the presence of multi-stability where both coherent and incoherent states coexist. We investigate such scenario in globally coupled populations of Kuramoto…
Based on recent advances in fibration symmetry theory, we investigate how structural symmetries influence synchronization in systems with higher-order interactions (HOI). Using bipartite graph representations, we identify a node partition…
We present an equation-free multi-scale approach to the computational study of the collective dynamics of the Kuramoto model [{\it Chemical Oscillations, Waves, and Turbulence}, Springer-Verlag (1984)], a prototype model for coupled…
In functionally complex systems, higher-order connectivity is often revealed in the underlying geometry of networked units. Furthermore, such systems often show signatures of self-organized criticality, a specific type of non-equilibrium…
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…
Higher-order interactions play a key role for the stability and function of a complex system. However, how to identify them is still an open problem. Here, we propose a method to fully reconstruct the structural connectivity of a system of…
Recently there has been an increasing interest in studying dynamical processes on networks exhibiting higher-order structures, such as simplicial complexes, where the dynamics acts above and beyond dyadic interactions. Using simulations or…
We study a simple two-dimensional swarmalator model that incorporates higher-order phase interactions, uncovering a diverse range of collective states. The latter include spatially coherent and gas-like configurations, neither of which…
In view of highly decentralized and diversified power generation concepts, in particular with renewable energies such as wind and solar power, the analysis and control of the stability and the synchronization of power networks is an…
We propose an infinite Kuramoto model for a countably infinite set of Kuramoto oscillators and study its emergent dynamics for two classes of network topologies. For a class of symmetric and row(or column)-summable network topology, we show…
Synchronization in various complex networks is significantly influenced by higher-order interactions combined with non-Gaussian stochastic perturbations, yet their mechanisms remain mainly unclear. In this paper, we systematically…
Higher-order interactions underlie complex phenomena in systems such as biological and artificial neural networks, but their study is challenging due to the scarcity of tractable models. By leveraging a generalisation of the maximum entropy…
We study the effect of network topology on the collective dynamics of an oscillator ensemble. Specifically, we explore explosive synchronization in a system of interacting star networks. Explosive synchronization is characterized by an…