Related papers: Exploring the phase diagrams of multidimensional K…
The Ott-Antonsen ansatz shows that, for certain classes of distribution of the natural frequencies in systems of $N$ globally coupled Kuramoto oscillators, the dynamics of the order parameter, in the limit $N\to \infty$, evolves, under…
We propose a Kuramoto model of coupled oscillators on a time-varying graph, whose dynamics is dictated by a Markov process in the space of graphs. The simplest representative is considering a base graph and then the subgraph determined by…
We derive a two-layer multiplex Kuramoto model from weakly coupled Wilson-Cowan oscillators on a cortical network with inhibitory synaptic time delays. Depending on the coupling strength and a phase shift parameter, related to cerebral…
A complete bifurcation analysis of explicit dynamical equations for the periodically forced Kuramoto model was performed in [L. M. Childs and S. H. Strogatz. Chaos 18 , 043128 (2008)], identifying all bifurcations within the model. We show…
The Kuramoto model has become a paradigm to describe the dynamics of nonlinear oscillator under the influence of external perturbations, both deterministic and stochastic. It is based on the idea to describe the oscillator dynamics by a…
This work considers the timescales associated with the global order parameter and the interlayer synchronization of coupled Kuramoto oscillators on multiplexes. For the two-layer multiplexes with initially high degree of synchronization in…
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…
We explore chaos in the Kuramoto model with multimodal distributions of the natural frequencies of oscillators and provide a comprehensive description under what conditions chaos occurs. For a natural frequency distribution with $M$ peaks…
We generalize the study of the noisy Kuramoto model, considered on a network of two interacting communities, to the case where the interaction strengths within and across communities are taken to be different in general. Using a geometric…
An ensemble of pulse-coupled phase-oscillators is thoroughly analysed in the presence of a mean-field coupling and a dispersion of their natural frequencies. In spite of the analogies with the Kuramoto setup, a much richer scenario is…
Synchronization is an omnipresent collective phenomenon in nature and technology, whose understanding is in particular for real-world systems still elusive. We study the synchronization transition in a phase oscillator system with two…
The dynamic phase transitions have been studied, within a mean-field approach, in the kinetic spin-1 Ising model Hamiltonian with arbitrary bilinear and biquadratic pair interactions in the presence of a time varying (sinusoidal) magnetic…
The Kuramoto model is a versatile mathematical framework that explains phenomena resulting from interactions among phase oscillators. It finds applications in various scientific and engineering domains. In this study, we focused on a…
We consider the two-dimensional (2D) noisy Kuramoto model of synchronization with short-range coupling and a Gaussian distribution of intrinsic frequencies, and investigate its ordering dynamics following a quench. We consider both…
The Kuramoto model is one of the most widely studied model for describing synchronization behaviors in a network of coupled oscillators, and it has found a wide range of applications. Finding all possible frequency synchronization…
We investigate the phase diagram of the Sakaguchi-Kuramoto model with a higher order interaction along with the traditional pairwise interaction. We also introduce asymmetry parameters in both the interaction terms and investigate the…
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.…
Bursting neurons fire rapid sequences of action potential spikes followed by a quiescent period. The basic dynamical mechanism of bursting is the slow currents that modulate a fast spiking activity caused by rapid ionic currents. Minimal…
Higher-order interactions fundamentally shape collective dynamics in oscillator networks. The topological Kuramoto model captures these effects by extending synchronization models to include interactions between cells of arbitrary dimension…
Orientation-rich images, such as fingerprints and textures, often exhibit coherent angular directional patterns that are challenging to model using standard generative approaches based on isotropic Euclidean diffusion. Motivated by the role…