We generalize the concept of local states (LS) for prediction high-dimensional, potentially mixed chaotic systems. The construction generalized (GLS) relies on defining distances between time series basis their (non-)linear correlations. demonstrate capabilities our approach based reservoir computing (RC) paradigm using Kuramoto-Sivashinsky (KS), Lorenz-96 (L96) and a combination both In system...

The Kuramoto model of coupled phase oscillators with inertia on Erdos-Renyi graphs is analyzed in this work. For a system intrinsic frequencies sampled from bimodal distribution we identify variety two cluster patterns and study their stability. To end, decompose the description dynamics into systems: one governing (macro) centers mass clusters second (micro) individual inside each cluster. for...

In this paper we present a novel approach to model perceptual grouping based on phase and frequency synchronization in a network of coupled Kuramoto oscillators. Transferring the grouping concept from the Competitive Layer Model (CLM) to a network of Kuramoto oscillators, we preserve the excellent grouping capabilities of the CLM, while dramatically improving the convergence rate, robustness to...

We prove that the Kuramoto-Sivashinsky equation is locally controllable in 1D and in 2D with one boundary control. Our method consists in combining several general results in order to reduce the nullcontrollability of this nonlinear parabolic equation to the exact controllability of a linear beam or plate system. This improves known results on the controllability of Kuramoto-Sivashinsky equatio...

Using a recently introduced linear reformulation of the Kuramoto model of self-synchronizing oscillator systems [1], we study a new class of analytically solvable oscillator systems defined by a particular coupling scheme. We show that these systems have a logarithmic scaling law in the vicinity of the critical point, which may be seen as anomalous with respect to the usual power-law behavior e...

We present a collective coordinate approach to describe coupled phase oscillators. We apply the method to study synchronisation in a Kuramoto model. In our approach, an N-dimensional Kuramoto model is reduced to an n-dimensional ordinary differential equation with n≪N, constituting an immense reduction in complexity. The onset of both local and global synchronisation is reproduced to good numer...