Related papers: Approximate solution for frequency synchronisation…
We investigate synchronization in a Kuramoto-like model with nearest neighbour coupling. Upon analyzing the behaviour of individual oscillators at the onset of complete synchronization, we show that the time interval between bursts in the…
We provide a comprehensive view of various phase transitions in random $K$-satisfiability problems solved by stochastic-local-search algorithms. In particular, we focus on the finite-size scaling (FSS) exponent, which is mathematically…
We study the synchronized behavior of the inertial Kuramoto oscillators with frustration effect under a symmetric and connected network. Due to the lack of second-order gradient flow structure and singularity of second-order derivative of…
We examine the impact of time delay on two coupled massive oscillators within the second-order Kuramoto model, which is relevant to the operations of real-world networks that rely on signal transmission speed constraints. Our analytical and…
We study the mean-field limit of the Kuramoto model of globally coupled oscillators. By studying the evolution in Fourier space and understanding the domain of dependence, we show a global stability result. Moreover, we can identify…
The Kuramoto model is a classical model used in the study of spontaneous synchronizations in networks of coupled oscillators. In this model, frequency synchronization configurations can be formulated as complex solutions to a system of…
Now a standard in Nonlinear Sciences, the Kuramoto model is the perfect example of the transition to synchrony in heterogeneous systems of coupled oscillators. While its basic phenomenology has been sketched in early works, the…
The multidimensional Kuramoto model describes the synchronization dynamics of particles moving on the surface of D-dimensional spheres, generalizing the original model where particles were characterized by a single phase. In this setup,…
In this paper, we will study the emergent behavior of Kuramoto model with frustration on a general digraph containing a spanning tree. We provide a sufficient condition for the emergence of asymptotical synchronization if the initial data…
We study the synchronization of a small-world network of identical coupled phase oscillators with Kuramoto interaction. First, we consider the model with instantaneous mutual interaction and the normalized coupling constant to the degree of…
We study synchronization properties of coupled oscillators on networks that allow description in terms of global mean field coupling. These models generalize the standard Kuramoto-Sakaguchi model, allowing for different contributions of…
The dynamics of ensembles of phase oscillators are usually described considering their infinite-size limit. In practice, however, this limit is fully accessible only if the Ott-Antonsen theory can be applied, and the heterogeneity is…
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…
The Kuramoto model of coupled phase oscillators on small-world (SW) graphs is analyzed in this work. When the number of oscillators in the network goes to infinity, the model acquires a family of steady state solutions of degree q, called…
A new collective behavior of resonant synchronization is discovered and the ability to retrieve information from brain memory is proposed based on this mechanism. We use modified Kuramoto phase oscillator to simulate the dynamics of a…
The Kuramoto-Sakaguchi model for coupled phase oscillators with phase-frustration is often studied in the thermodynamic limit of infinitely many oscillators. Here we extend a model reduction method based on collective coordinates to capture…
We study a Kuramoto model in which the oscillators are associated with the nodes of a complex network and the interactions include a phase frustration, thus preventing full synchronization. The system organizes into a regime of remote…
We study the chaotic behavior of the synchronization phase transition in the Kuramoto model. We discuss the relationship with analogous features found in the Hamiltonian Mean Field (HMF) model. Our numerical results support the connection…
Many real-world systems of coupled agents exhibit directed interactions, meaning that the influence of an agent on another is not reciprocal. Furthermore, interactions usually do not have identical amplitude and/or sign. To describe…
We show that for the Kuramoto model (with identical phase oscillators equally coupled) its global statistics and size of the basins of attraction can be estimated through the eigenvalues of all stable (frequency) synchronized states. This…