We propose a new model of opinion formation, the Opinion Changing Rate (OCR) model. Instead of investigating the conditions that allow consensus in a world of agents with different opinions, we study under which conditions a group of agents with a different natural tendency (rate) to change opinion can find agreement. The OCR is a modified version of the Kuramoto model, one of the simplest mode...

We study the relationship between chaotic behavior and the violation of the Central Limit Theorem (CLT) in the Kuramoto model. We calculate sums of angles at equidistant times along deterministic trajectories of single oscillators and we show that, when chaos is sufficiently strong , the Pdfs of the sums tend to a Gaussian, consistently with the standard CLT. On the other hand, when the system ...

We examine the dynamics of the Kuramoto model with a new analytical approach. By defining an appropriate set of moments the dynamical equations can be exactly closed. We discuss some applications of the formalism such as the existence of an effective Hamiltonian for the dynamics. We also show how this approach can be used to numerically investigate the dynamical behaviour of the model without f...

A non-isotropic version of phase equations such as the Burgers equation, the K-dV-Burgers equation, the Kuramoto-Sivashinsky equation and the Benney equation in the three-dimensional space is systematically derived from a general reaction-diffusion system by means of the renormalization group method. PACS codes: 47.20.Ky

Résumé. Nous considérons l’équation de Kuramoto–Sivashinskymunie de conditions aux limites périodiques et d’une donnée initiale. Nous l’approchons en utilisant une méthode d’éléments finis de type Galerkin pour la discrétisation en espace, et un schéma de Runge–Kutta implicite pour la discrétisation en temps. Nous obtenons des estimations d’erreur optimales et discutons de la linéarisation de c...

The mean-field Kuramoto model for synchronization of phase oscillators with an asymmetric bimodal frequency distribution is analyzed. Breaking the reflection symmetry facilitates oscillator synchronization to rotating wave phases. Numerical simulations support the results based of bifurcation theory and high-frequency calculations. In the latter case, the order parameter is a linear superpositi...

A continuum model, based on the damped Kuramoto-Sivashinsky equation, is shown to reproduce the morphology evolution during ion sputtering quite successfully. In a very narrow range of the damping parameter a , the alignment of the structures into hexagonal domains is obtained under normal incidence of ions with striking resemblance to the experimentally observed dot patterns. The origin of thi...

We introduce a new variational method for finding periodic orbits of flows and spatio-temporally periodic solutions of classical field theories, a generalization of the Newton method to a flow in the space of loops. The feasibility of the method is demonstrated by its application to several dynamical systems, including the Kuramoto-Sivashinsky system.

We analyze the discretization of the periodic initial value problem for Kuramoto–Sivashinsky type equations with Burgers nonlinearity by implicit– explicit backward difference formula (BDF) methods, establish stability and derive optimal order error estimates. We also study discretization in space by spectral methods.

We prove a convergence result for the standard Kuramoto model with all-to-all coupling. Specifically, we show that the critical coupling strength associated with the onset of completely phase-locked behaviour converges in probability as the number of oscillators tends to infinity.