Related papers: Synchronization Behavior in a Ternary Phase Model
We report experimental evidence of the route to spatiotemporal chaos in a large 1D-array of hotspots in a thermoconvective system. Increasing the driving force, a stationary cellular pattern becomes unstable towards a mixed pattern of…
The synchronization pattern of a fully connected competing Kuramoto model with a uniform intrinsic frequency distribution $g(\omega)$ was recently considered. This competing Kuramoto model assigns two coupling constants with opposite signs,…
Output feedback controlled synchronization problems for a class of nonlinear unstable systems under information constraints imposed by limited capacity of the communication channel are analyzed. A binary time-varying coder-decoder scheme is…
We investigate the emergence of synchronization in the second-order Kuramoto model with adaptive simplicial interactions on a globally connected network. This inertial Kuramoto framework describes systems, where oscillator frequencies…
The effects of disorder in external forces on the dynamical behavior of coupled nonlinear oscillator networks are studied. When driven synchronously, i.e., all driving forces have the same phase, the networks display chaotic dynamics. We…
Synchronization of an ensemble of oscillators is an emergent phenomenon present in several complex systems, ranging from social and physical to biological and technological systems. The most successful approach to describe how coherent…
We study synchronization of locally coupled noisy phase oscillators which move diffusively in a one-dimensional ring. Together with the disordered and the globally synchronized states, the system also exhibits several wave-like states which…
We establish a unified synchronization framework for the all-to-all hybrid Kuramoto model that couples first- and second-order oscillators within a single dynamical system. Although the Kuramoto model has become one of the most widely used…
We consider a semi-classical nonlinear Schrodinger equation. For initial data causing focusing at one point in the linear case, we study a nonlinearity which is super-critical in terms of asymptotic effects near the caustic. We prove the…
The celebrated Kuramoto model provides an analytically tractable framework to study spontaneous collective synchronization and comprises globally coupled limit-cycle oscillators interacting symmetrically with one another. The…
Turbulent systems exhibit a remarkable multi-scale complexity, in which spatial structures induce scale-dependent statistics with strong departures from Gaussianity. In Fourier space, this is reflected by pronounced phase synchronization. A…
Synchronization transition in oscillatory networks manifests itself as the appearance of a periodic global mode. While perfect in the thermodynamic limit, this mode fluctuates for finite ensembles. We characterize the coherence of this mode…
Theoretical studies of synchronization are usually based on models of coupled phase oscillators which, when isolated, have constant angular frequency. Stochastic discrete versions of these uniform oscillators have also appeared in the…
Global and partial synchronization are the two distinctive forms of synchronization in coupled oscillators and have been well studied in the past decades. Recent attention on synchronization is focused on the chimera state (CS) and…
We have compared the phase synchronization transition of the second order Kuramoto model on 2D lattices and on large, synthetic power grid networks, generated from real data. The latter are weighted, hierarchical modular networks. Due to…
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…
Sufficient conditions for synchronization of coupled Lienard-type oscillators are investigated via averaging technique. Coupling considered here is pairwise, unidirectional, and described by a nonlinear function (whose graph resides in the…
In heterogeneous networks of coupled oscillators, phase frustration typically prevents the emergence of synchronization in the Sakaguchi--Kuramoto (SK) model. In this study, we propose an analytical framework to overcome this barrier and…
Brain networks typically exhibit characteristic synchronization patterns where several synchronized clusters coexist. On the other hand, neurological disorders are considered to be related to pathological synchronization such as excessive…
In this paper, we propose an $N$ oscillators Kuramoto model with quaternions $\mathbb{H}$. In case the coupling strength is strong, a sufficient condition of synchronization is established for general $N\geqslant 2$. On the other hand, we…