相关论文: Finite-size scaling of the Kuramoto model at criti…
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…
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…
The entrainment transition of coupled random frequency oscillators presents a long-standing problem in nonlinear physics. The onset of entrainment in populations of large but finite size exhibits strong sensitivity to fluctuations in the…
The Kuramoto model, a paradigmatic framework for studying synchronization, exhibits a transition to collective oscillations only above a critical coupling strength in the thermodynamic limit. However, real-world systems are finite, and…
The Kuramoto model, which serves as a paradigm for investigating synchronization phenomenon of oscillatory system, is known to exhibit second-order, i.e., continuous, phase transitions in the macroscopic order parameter. Here, we generalize…
Scientists have been considering the Kuramoto model to understand the mechanism behind the appearance of collective behaviour, such as frequency synchronisation (FS) as a paradigm, in real-world networks with a finite number of oscillators.…
We present a systematic analysis of dynamic scaling in the time evolution of the phase order parameter for coupled oscillators with non-identical natural frequencies in terms of the Kuramoto model. This provides a comprehensive view of…
Finite-size effects in the Kuramoto model are known to induce collective fluctuations even below the critical coupling, where the thermodynamic limit predicts complete asynchrony. While the shot-noise approach developed in our recent work…
The onset of synchronization in a system of random frequency oscillators coupled through a random network is investigated. Using a mean-field approximation, we characterize sample-to-sample fluctuations for networks of finite size, and…
The Kuramoto model provides a concrete mathematical realization of emergent synchrony in a population of phase-coupled oscillators. Since Kuramoto's publication, \textit{Oscillations, Waves, and Turbulence}, researchers have worked to…
We develop an ab initio approach to describe the statistical behavior of finite-size fluctuations in the deterministic Kuramoto-Sakaguchi model. We obtain explicit expressions for the covariance function of fluctuations of the complex order…
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.…
The incoherent state of the Kuramoto model of coupled oscillators exhibits marginal modes in mean field theory. We demonstrate that corrections due to finite size effects render these modes stable in the subcritical case, i.e. when the…
We investigate the finite-size effects on the dynamical evolution of the Kuramoto model with inertia coupled through triadic interactions. Our findings reveal that fluctuations resulting from the finite size drive the system toward a…
We provide an analysis of the classic Kuramoto model of coupled nonlinear oscillators that goes beyond the existing results for all-to-all networks of identical oscillators. Our work is applicable to oscillator networks of arbitrary…
We study phase locking in the Kuramoto model of coupled oscillators in the special case where the number of oscillators, $N$, is large but finite, and the oscillators' natural frequencies are evenly spaced on a given interval. In this case,…
The entrainment transition of coupled random frequency oscillators is revisited. The Kuramoto model (global coupling) is shown to exhibit unusual sample-dependent finite size effects leading to a correlation size exponent $\bar\nu=5/2$.…
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,…
The Kuramoto model has been introduced to describe synchronization phenomena observed in groups of cells, individuals, circuits, etc. The model consists of $N$ interacting oscillators on the one dimensional sphere $\mathbf{S}^{1}$, driven…
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…