Related papers: Critical dynamics of the Kuramoto model on sparse …
Explosive synchronization can be observed in scale-free networks when Kuramoto oscillators have natural frequencies equal to their number of connections. In the current work, we took into account mean-field approximations to determine the…
Completely random measures (CRMs) are fundamental to Bayesian nonparametric models, with applications in clustering, feature allocation, and network analysis. A key quantity of interest is the Laplace exponent, whose asymptotic behavior…
For any network of identical Kuramoto oscillators with identical positive coupling, there is a critical connectivity above which the system is guaranteed to converge to the in-phase synchronous state, for almost all initial conditions. But…
We present an alternative approach to finite-size effects around the synchronization transition in the standard Kuramoto model. Our main focus lies on the conditions under which a collective oscillatory mode is well defined. For this…
Many real-world examples of distributed oscillators involve not only time delays but also attractive (positive) and repulsive (negative) influences in their network interactions. Here, considering such examples, we generalize the Kuramoto…
The Kuramoto model is a classical mathematical model in the field of non-linear dynamical systems that describes the evolution of coupled oscillators in a network that may reach a synchronous state. The relationship between the network's…
Synchronization is observed in many natural systems, with examples ranging from neuronal activation to walking pedestrians. The models proposed by Winfree and Kuramoto stand as the classic frameworks for investigating these phenomena. The…
We study populations of oscillators, all-to-all coupled by means of quenched disordered phase shifts. While there is no traditional synchronization transition with a nonvanishing Kuramoto order parameter, the system demonstrates a specific…
One of a classical synchronization model is the Kuramoto model. We propose both first and second order Kuramoto dynamical models on graphs using discrete optimal transport dynamics. We analyze the synchronization behaviors for some examples…
The critical behaviour of statistical models with long-range interactions exhibits distinct regimes as a function of $\rho$, the power of the interaction strength decay. For $\rho$ large enough, $\rho>\rho_{\rm sr}$, the critical behaviour…
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…
The high-dimensional generalization of the one-dimensional Kuramoto paradigm has been an essential step in bringing about a more faithful depiction of the dynamics of real-world systems. Despite the multi-dimensional nature of the…
By means of numerical integration we investigate the coherent and incoherent phases in a generalized Kuramoto model of phase-coupled oscillators with distance-dependent delay. Preserving the topology of a complete graph, we arrange the…
A recently proposed dimensional reduction approach for studying synchronization in the Kuramoto model is employed to build optimal network topologies to favor or to suppress synchronization. The approach is based in the introduction of a…
We revisit the Kuramoto model to explore the finite-size scaling (FSS) of the order parameter and its dynamic fluctuations near the onset of the synchronization transition, paying particular attention to effects induced by the randomness of…
We consider the Kuramoto model of coupled oscillators, specifically the case of tree networks, for which we prove a simple closed-form expression for the critical coupling. For several classes of tree, and for both uniform and Gaussian…
We investigate the synchronization transition of the Shinomoto-Kuramoto model on networks of the fruit-fly and two large human connectomes. This model contains a force term, thus is capable of describing critical behavior in the presence of…
Maintaining the stability of synchronization state is crucial for the functioning of many natural and artificial systems. In this study, we develop methods to optimize the synchronization stability of the Kuramoto model by minimizing the…
The Kuramoto model is fundamental to the study of synchronization. It consists of a collection of oscillators with interactions given by a network, which we identify respectively with vertices and edges of a graph. In this paper, we show…
We study the kinetic Kuramoto model for coupled oscillators with coupling constant below the synchronization threshold. We manage to prove that, for any analytic initial datum, if the interaction is small enough, the order parameter of the…