The calculation of order parameters to characterize the degree of synchronization usually requires the measurement of time series of observable quantities for all individual dynamical elements. In this article, a new method of extracting the Kuramoto order from global measurements for weakly coupled, nearly identical oscillators is established and successfully tested with electrochemical popula...

Abstract. Periodic eigendecomposition algorithm for calculating eigenvectors of a periodic product of a sequence of matrices, an extension of the periodic Schur decomposition, is formulated and compared with the recently proposed covariant vectors algorithms. In contrast to those, periodic eigendecomposition requires no power iteration and is capable of determining not only the real eigenvector...

We consider the family of destabilized Kuramoto-Sivashinsky equations in one spatial dimension ut + νuxxxx + βuxx + γuux = αu for α,ν ≥ 0 and β ,γ ∈ R. For certain parameter values, shock-like stationary solutions have been numerically observed. In this work we verify the existence of several such solutions using the framework of self-consistent bounds and validated numerics.

Synchronization is a common phenomenon in physical and biological systems. We examine the synchronization of two ~and more! metronomes placed on a freely moving base. The small motion of the base couples the pendulums causing synchronization. The synchronization is generally in-phase, with antiphase synchronization occurring only under special conditions. The metronome system provides a mechani...

In this letter we discuss use of Granger causality to the analyze systems of coupled circular variables, by modifying a recently proposed method for multivariate analysis of causality. We show the application of the proposed approach on several Kuramoto systems, in particular one living on networks built by preferential attachment and a model for the transition from deeply to lightly anaestheti...

In this article, we present an inverse problem for the nonlinear 1-d Kuramoto-Sivashinsky (K-S) equation. More precisely, we study the nonlinear inverse problem of retrieving the anti-diffusion coefficient from the measurements of the solution on a part of the boundary and also at some positive time in the whole space domain. The Lipschitz stability for this inverse problem is our main result a...

In this note, we announce a general result resolving the long-standing question of nonlinear modulational stability, or stability with respect to localized perturbations, of periodic travelingwave solutions of the generalized Kuramoto–Sivashinski equation, establishing that spectral modulational stability, defined in the standard way, implies nonlinear modulational stability with sharp rates of...

We present the long-time dynamics of unidirectionally coupled identical Kuramoto oscillators in a ring, when each oscillator is influenced sinusoidally by a single preassigned oscillator. In this situation, for a large system with N ≥ 5, it is well known that the synchronized states and the splay-state are the only stable equilibria by Gershgorin’s theorem and linear stability analysis, whereas...

Recent developments of the multiplex paradigm included efforts to understand the role played by the presence of several layers on the dynamics of processes running on these networks. The possible existence of new phenomena associated to the richer topology has been discussed and examples of these differences have been systematically searched. Here, we show that the interconnectivity of the laye...