Related papers: Quantum Effects on the Synchronization Dynamics of…
Phase reduction is a powerful technique in the study of nonlinear oscillatory systems. Under certain assumptions, it allows us to describe each multidimensional oscillator by a single phase variable, giving rise to simple phase models such…
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…
We study a Kuramoto-like model of coupled identical phase oscillators on a network, where attractive and repulsive couplings are balanced dynamically due to nonlinearity in interaction. Under a week force, an oscillator tends to follow the…
We consider the nonlinear extension of the Kuramoto model of globally coupled phase oscillators where the phase shift in the coupling function depends on the order parameter. A bifurcation analysis of the transition from fully synchronous…
We study a nonlinear partial differential equation that arises when introducing inertial effects in the Kuramoto model. Based on the known theory of degenerate Kolmogorov operators, we prove existence, uniqueness and a priori estimates of…
The Kuramoto model was recently extended to arbitrary dimensions by reinterpreting the oscillators as particles moving on the surface of unit spheres in a D-dimensional space. Each particle is then represented by a D-dimensional unit…
Models of coupled oscillator networks play an important role in describing collective synchronization dynamics in biological and technological systems. The Kuramoto model describes oscillator's phase evolution and explains the transition…
The conditions under which synchronization is achieved for a one-dimensional ring of identical phase oscillators with Kuramoto-like local coupling are studied. The system is approached in the weakly coupled approximation as phase units.…
Randomly coupled phase oscillators may synchronize into disordered patterns of collective motion. We analyze this transition in a large, fully connected Kuramoto model with symmetric but otherwise independent random interactions. Using the…
We study synchronization phenomenon in a self-correcting population of noisy phase oscillators with randomly distributed natural frequencies. In our model each oscillator stochastically switches its phase to the ensemble-averaged value…
We present a study of the critical phenomena around the quantum critical point in heavy-fermion systems. In the framework of the S=1/2 Kondo lattice model, we introduce an extended decoupling scheme of the Kondo interaction which allows one…
Spontaneous synchronisation is a collective phenomenon that can occur in both dynamical classical and quantum systems. Here, we analyse the spontaneous synchronisation dynamics of vibrations assisting energy transfer in a bio-inspired…
Macroscopic ensembles of radiating dipoles are ubiquitous in the physical and natural sciences. In the classical limit the dipoles can be described as damped-driven oscillators, which are able to spontaneously synchronize and collectively…
Synchronization of coupled oscillators is often described using the Kuramoto model. Here we study a generalization of the Kuramoto model where oscillators communicate with each other through an external medium. This generalized model…
After decades of study, there are only two known mechanisms to induce global synchronization in a population of oscillators: deterministic coupling and common forcing. The inclusion of independent random forcing in these models typically…
We introduce a novel coupling scheme for maximizing the synchronization of Kuramoto oscillator networks under a fixed coupling budget. We show that by scaling the interaction strength between oscillators according to their frequency…
In his classical work on synchronization, Kuramoto derived the formula for the critical value of the coupling strength corresponding to the transition to synchrony in large ensembles of all-to-all coupled phase oscillators with randomly…
We present a novel interdisciplinary framework that bridges synchronization theory and multi-agent AI systems by adapting the Kuramoto model to describe the collective dynamics of heterogeneous AI agents engaged in complex task execution.…
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…
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…