Related papers: The size of the sync basin resolved
Phase-locked states with a constant phase shift between the neighboring oscillators are studied in rings of identical Kuramoto oscillators with time-delayed nearest-neighbor coupling. The linear stability of these states is derived and it…
In dynamical systems, the full stability of fixed point solutions is determined by their basin of attraction. Characterizing the structure of these basins is, in general, a complicated task, especially in high dimensionality. Recent works…
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…
To explore basin geometry in high-dimensional dynamical systems, we consider a ring of identical Kuramoto oscillators. Many attractors coexist in this system; each is a twisted periodic orbit characterized by a winding number $q$, with…
We investigate the global basin structure of twisted states in nearest-neighbor coupled phase oscillators with a common phase shift $\alpha$. As $\alpha$ increases, basin boundaries become progressively more complex, with their fractal…
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…
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…
We solve a longstanding stability problem for the Kuramoto model of coupled oscillators. This system has attracted mathematical attention, in part because of its applications in fields ranging from neuroscience to condensed-matter physics,…
We consider the Kuramoto model on a graph with nodes given by $n$ i.i.d. points uniformly distributed on the $d$ dimensional torus. Two nodes are declared neighbors if they are at distance less than $\epsilon$. We prove a scaling limit for…
We study a nonlocal diffusion equation approximating the dynamics of coupled phase oscillators on large graphs. Under appropriate assumptions, the model has a family of steady state solutions called twisted states. We prove a sufficient…
Synchronization is a ubiquitous phenomenon in complex systems. The Kuramoto model serves as a paradigmatic framework for understanding how coupled oscillators achieve collective rhythm. Conventional approaches focus on pairwise…
Zhang and Strogatz [Phys. Rev. Lett. 127, 194101 (2021)] used high-dimensional simulations to argue that basins of attraction in the Kuramoto ring are octopus-like: their volume scales as $e^{-kq^2}$ in the winding number $q$, nearly all of…
It is common that the average length of chaotic transients appearing as a consequence of crises in dynamical systems obeys a power low of scaling with the distance from the crisis point. It is, however, only a rough trend; in some cases…
Synchronization in systems of coupled Kuramoto oscillators may depend on their natural frequencies, coupling, and underlying networks. In this paper, we reduce the alternatives to only one by considering identical oscillators where the only…
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…
Many studies of synchronization properties of coupled oscillators, based on the classical Kuramoto approach, focus on ensembles coupled via a mean field. Here we introduce a setup of Kuramoto-type phase oscillators coupled via two mean…
The Kuramoto model (KM) of $n$ coupled phase-oscillators is analyzed in this work. The KM on a Cayley graph possesses a family of steady state solutions called twisted states. Topologically distinct twisted states are distinguished by the…
A modified Kuramoto model of synchronization in a finite discrete system of locally coupled oscillators is studied. The model consists of N oscillators with random natural frequencies arranged on a ring. It is shown analytically and…
A two-dimensional lattice of oscillators with identical (zero) intrinsic frequencies and Kuramoto type of interactions with randomly frustrated couplings is considered. Starting the time evolution from slightly perturbed synchronized…
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…