Related papers: Approximate solution for frequency synchronisation…
The Kuramoto model for an ensemble of coupled oscillators provides a paradigmatic example of non-equilibrium transitions between an incoherent and a synchronized state. Here we analyze populations of almost identical oscillators in…
We generalize the Kuramoto model for coupled phase oscillators by allowing the frequencies to drift in time according to Ornstein-Uhlenbeck dynamics. Such drifting frequencies were recently measured in cellular populations of circadian…
The agent-based singular Kuramoto model was proposed in [60] as a singular version of the Kuramoto model of coupled oscillators that is consistent with Hebb's rule of neuroscience. In such paper, the authors studied its well-posedness via…
We establish a unified synchronization framework for the all-to-all hybrid Kuramoto model that couples first- and second-order oscillators within a single dynamical system. Although the Kuramoto model has become one of the most widely used…
In the context of the celebrated Kuramoto model of globally-coupled phase oscillators of distributed natural frequencies, which serves as a paradigm to investigate spontaneous collective synchronization in many-body interacting systems, we…
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…
We present a rigorous mathematical framework establishing the equivalence of four classical notions of synchronization full phase-locking, phase-locking, frequency synchronization, and order parameter synchronization in generalized Kuramoto…
Using the main results of the Kuramoto theory of globally coupled phase oscillators combined with methods from probability and generalized function theory in a geometric analysis, we extend Kuramoto's results and obtain a mathematical…
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…
Determining the number of stable phase-locked solutions for locally coupled Kuramoto models is a long-standing mathematical problem with important implications in biology, condensed matter physics and electrical engineering among others. We…
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…
Kuramoto model is one of the most prominent models for the synchronization of coupled oscillators. It has long been a research hotspot to understand how natural frequencies, the interaction between oscillators, and network topology…
The Kuramoto model describes the synchronization of coupled oscillators that have different natural frequencies. Among the many generalizations of the original model, Kuramoto and Sakaguchi (KS) proposed a {\it frustrated} version that…
We study the global bifurcations of frequency weighted Kuramoto model in low-dimension for network of fully connected oscillators. To study the effect of non-zero-centered frequency distribution, we consider two symmetric Lorentzians as an…
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 transient stability of power systems and synchronization of non-uniform Kuramoto oscillators are closely related problems. In this paper, we develop a novel regional stability analysis framework based on the proposed region-parametrized…
We study the emergence of synchronization in the Kuramoto model on a digraph in the presence of time delays. Assuming the digraph is strongly connected, we first establish a uniform bound on the phase diameter and subsequently prove the…
Synchronization in networks of coupled oscillators is a widely studied topic with extensive scientific and engineering applications. In this paper, we study the frequency synchronization problem for networks of Kuramoto oscillators with…
A family of stochastic processes has quasi-cycle oscillations if the oscillations are sustained by noise. For such a family we define a Kuramoto-type coupling of both phase and amplitude processes. We find that synchronization, as measured…
We show that self-consistent partial synchrony in globally coupled oscillatory ensembles is a general phenomenon. We analyze in detail appearance and stability properties of this state in possibly the simplest setup of a biharmonic…