Related papers: A parametrisation method for high-order phase redu…
This paper provides an $H_2$ optimal scheme for reducing diffusively coupled second-order systems evolving over undirected networks. The aim is to find a reduced-order model that not only approximates the input-output mapping of the…
Networks of coupled nonlinear oscillators can display a wide range of emergent behaviours under variation of the strength of the coupling. Network equations for pairs of coupled oscillators where the dynamics of each node is described by…
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…
Collective behaviors of populations of coupled oscillators have attracted much attention in recent years. In this paper, an order parameter approach is proposed to study the low-dimensional dynam- ical mechanism of collective…
We present a method for reconstructing resonant interactions in weakly coupled phase oscillator systems from noisy time series. Instead of attempting to recover the full phase equations, which may be non-identifiable in the presence of…
We study synchronization in delay-coupled oscillator networks, using a master stability function approach. Within a generic model of Stuart-Landau oscillators (normal form of super- or subcritical Hopf bifurcation) we derive analytical…
Employing both Bayesian statistics and the theory of nonlinear dynamics, we present a practically efficient method to extract a phase description of weakly coupled limit-cycle oscillators directly from time series observed in a rhythmic…
We perform a stochastic model reduction of the Kuramoto-Sakaguchi model for finitely many coupled phase oscillators with phase frustration. Whereas in the thermodynamic limit coupled oscillators exhibit stationary states and a constant…
The coupled Stuart-Landau equation serves as a fundamental model for exploring synchronization and emergent behavior in complex dynamical systems. However, understanding its dynamics from a comprehensive nonlinear perspective remains…
We present a study dealing with a novel phase reconstruction method based on iterated Hilbert transform embeddings. We show results for the Stuart-Landau oscillator observed by generic observables. The benefits for reconstruction of the…
Phase reduction is a powerful technique that makes possible describe the dynamics of a weakly perturbed limit-cycle oscillator in terms of its phase. For ensembles of oscillators, a classical example of phase reduction is the derivation of…
The aim of this work is to provide asymptotic estimates for the splitting of separatrices in a perturbed 3-degree-of-freedom Hamiltonian system, associated to a 2-dimensional whiskered torus (invariant hyperbolic torus) whose frequency…
We present a phase-amplitude reduction framework for analyzing collective oscillations in networked dynamical systems. The framework, which builds on the phase reduction method, takes into account not only the collective dynamics on the…
Quasi-periodic trajectories with two or more incommensurate frequencies are ubiquitous in nonlinear dynamics, yet the classical Fourier-based time-spectral method is tied to strictly periodic responses. We introduce a torus time-spectral…
We propose a new class of high-order time-marching schemes with dissipation user-control and unconditional stability for parabolic equations. High-order time integrators can deliver the optimal performance of highly-accurate and robust…
A novel regime of synchronization, called remote synchronization, where the peripheral nodes form a phase synchronized cluster not including the hub, was recently observed in star motifs. We show the existence of a more general dynamical…
A method is presented for tracing the locus of a specific peak in the frequency response under variation of a parameter. It is applicable to periodic, steady-state vibrations of harmonically forced nonlinear mechanical systems. It operates…
We study control of synchronization in weakly coupled oscillator networks by using a phase reduction approach. Starting from a general class of limit cycle oscillators we derive a phase model, which shows that delayed feedback control…
This technical note deals with the problem of asymptotically stabilizing the splay state configuration of a network of identical pulse coupled oscillators through the design of the their phase response function. The network of pulse coupled…
We propose a coupled system of fast and slow phase oscillators. We observe two-step transitions to quasi-periodic motions by direct numerical simulations of this coupled oscillator system. A low-dimensional equation for order parameters is…