Related papers: Kuramoto model with frequency-degree correlations …
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…
We present a detailed analysis of the stability of synchronized solutions to the Kuramoto system of oscillators. We derive an analytical expression counting the dimension of the unstable manifold associated to a given stationary solution.…
In this study, we present a general framework for comparing two dynamical processes that describe the synchronization of oscillators coupled through networks of the same size. We introduce a measure of dissimilarity defined in terms of a…
We introduce and investigate the effects of a new class of stochastic resetting protocol called subsystem resetting, whereby a subset of the system constituents in a many-body interacting system undergoes bare evolution interspersed with…
In this paper, we study the synchronization of identical Kuramoto phase oscillators under cumulative stochastic damage to the edges of networks. We analyze the capacity of coupled oscillators to reach a coherent state from initial random…
We have compared the phase synchronization transition of the second order Kuramoto model on 2D lattices and on large, synthetic power grid networks, generated from real data. The latter are weighted, hierarchical modular networks. Due to…
We investigate the role of the spectral dimension $d_s$ in determining the universality of phase transitions on a complex network. Due to its structural heterogeneity, a complex network generally acts as a disordered system. Specifically,…
This work presents a frequency multiplexed 3-limit cycles network in a multimode microelectromechanical nonlinear resonator. The network is composed of libration limit cycles and behaves in an analogous manner to a phase oscillator network.…
It has been recently reported that explosive synchronization transitions can take place in networks of phase oscillators [G\'omez-Garde\~nes \emph{et al.} Phys.Rev.Letts. 106, 128701 (2011)] and chaotic oscillators [Leyva \emph{et al.}…
In this work we study the dynamics of Kuramoto oscillators on a stochastically evolving network whose evolution is governed by the phases of the individual oscillators and degree distribution. Synchronization is achieved after a threshold…
Explosive synchronization (ES) of coupled oscillators on networks is shown to be originated from existence of correlation between natural frequencies of oscillators and degrees of corresponding nodes. Here, we demonstrate that ES is a…
A generalized Kuramoto model of coupled phase oscillators with slowly varying coupling matrix is studied. The dynamics of the coupling coefficients is driven by the phase difference of pairs of oscillators in such a way that the coupling…
In the Kuramoto model, a uniform distribution of the natural frequencies leads to a first-order (i.e., discontinuous) phase transition from incoherence to synchronization, at the critical coupling parameter $K_c$. We obtain the asymptotic…
We investigate the emergence of synchronization in the second-order Kuramoto model with adaptive simplicial interactions on a globally connected network. This inertial Kuramoto framework describes systems, where oscillator frequencies…
The mean field Kuramoto model describing the synchronization of a population of phase oscillators with a bimodal frequency distribution is analyzed (by the method of multiple scales) near regions in its phase diagram corresponding to…
We prove that in a coupled Kuramoto oscillator network at stable equilibrium, the physical phase displacement under weak output nudging is the gradient of the loss with respect to natural frequencies, with equality as the nudging strength…
The mean-field Kuramoto model for synchronization of phase oscillators with an asymmetric bimodal frequency distribution is analyzed. Breaking the reflection symmetry facilitates oscillator synchronization to rotating wave phases. Numerical…
Oscillatory networks subjected to noise are broadly used to model physical and technological systems. Due to their nonlinear coupling, such networks typically have multiple stable and unstable states that a network might visit due to noise.…
Phase balanced states are a highly under-explored class of solutions of the Kuramoto model and other coupled oscillator models on networks. So far, coupled oscillator research focused on phase synchronized solutions. Yet, global constraints…
Dynamics of complex systems are often driven by interactions that extend beyond pairwise links, underscoring the need to establish a correspondence between interpretable system parameters and emergent phenomena in hypergraph-based networks.…