Related papers: From phase to amplitude oscillators
We study dynamics of populations of resonantly coupled oscillators having different frequencies. Starting from the coupled van der Pol equations we derive the Kuramoto-type phase model for the situation, where the natural frequencies of two…
A density oscillator is a fluid system in which oscillatory flow occurs between different density fluids through the pore connecting them. We investigate the synchronization in coupled density oscillators using two-dimensional hydrodynamic…
Recently, the first-order synchronization transition has been studied in systems of coupled phase oscillators. In this paper, we propose a framework to investigate the synchronization in the frequency-weighted Kuramoto model with all-to-all…
An Ott-Antonsen reduced $M$-population of Kuramoto-Sakaguchi oscillators is investigated, focusing on the influence of the phase-lag parameter $\alpha$ on the collective dynamics. For oscillator populations coupled on a ring, we obtained a…
An ensemble of uncoupled limit-cycle oscillators receiving common Poisson impulses shows a range of non-trivial behavior, from synchronization, desynchronization, to clustering. The group behavior that arises in the ensemble can be…
Two decades ago, a phenomenon resembling Landau damping was described in the synchronization of globally coupled oscillators: the evidence of a regime where the order parameter decays when linear theory predicts neutral stability for the…
Using an expansion in order parameters, the equation of motion for the centroid of globally coupled oscillators with natural frequencies taken from a distribution is obtained for the case of high coupling, low dispersion of natural…
The Stuart-Landau oscillator generalized to $D > 2$ dimensions has SO($D$) rotational symmetry. We study the collective dynamics of a system of $K$ such oscillators of dimensions $D =$ 3 and 4, with coupling chosen to either preserve or…
We consider a population of two-dimensional oscillators with random couplings, and explore the collective states. The coupling strength between oscillators is randomly quenched with two values one of which is positive while the other is…
We outline a general theory for the analysis of flow-distributed standing and travelling wave patterns in one-dimensional, open plug-flows of oscillatory chemical media. We treat both the amplitude and phase dynamics of small and…
This article studies stochastic relative phase stability, i.e., stochastic phase-cohesiveness, of discrete-time phase-coupled oscillators. Stochastic phase-cohesiveness in two types of networks is studied. First, we consider oscillators…
We study the collective dynamics of identical phase oscillators on globally coupled networks whose interactions are asymmetric and mediated by positive and negative couplings. We split the set of oscillators into two interconnected…
We analyse the collective behavior of a mean-field model of phase-oscillators of Kuramoto-Daido type coupled through pairwise interactions which depend on phase differences: the coupling function is composed of three harmonics. We provide…
The effect of a temporal modulation at three times the critical frequency on a Hopf bifurcation is studied in the framework of amplitude equations. We consider a complex Ginzburg-Landau equation with an extra quadratic term, resulting from…
Random Phase Approximation (RPA) provides a very convenient tool to study the ensembles of weakly interacting waves, commonly called Wave Turbulence. In its traditional formulation, RPA assumes that phases of interacting waves are random…
Partial synchronous states appear between full synchrony and asynchrony and exhibit many interesting properties. Most frequently, these states are studied within the framework of phase approximation. The latter is used ubiquitously to…
We analyze the collective behavior of a lattice model of pulse-coupled oscillators. By means of computer simulations we find the relation between the intrinsic dynamics of each member of the population and their mutual interaction that…
A model of clustering dynamics is proposed for a population of spatially distributed active rotators. A transition from excitable to oscillatory dynamics is induced by the increase of the local density of active rotators. It is interpreted…
The role of a new form of dynamic interaction is explored in a network of generic identical oscillators. The proposed design of dynamic coupling facilitates the onset of a plethora of asymptotic states including synchronous states,…
We explore oscillatory behaviour in a family of periodically driven spin chains which are subject to a weak measurement followed by post-selection. We discover a transition to an oscillatory phase as the strength of the measurement is…