Related papers: Order parameter analysis of synchronization transi…
Coupled phase-oscillators are important models related to synchronization. Recently, Ott-Antonsen(OA) ansatz is developed and used to get low-dimensional collective behaviors in coupled oscillator systems. In this paper, we develop a simple…
The OA ansatz has attracted much attention recently, infinite-dimensional Kuramoto model could collapses to a two-dimensional system of order differential equations with it. In this paper, we propose the ensemble order parameter (EOP)…
In this paper, we propose a framework to investigate the collective dynamics in ensembles of globally coupled phase oscillators when higher-order modes dominate the coupling. The spatiotemporal properties of the attractors in various…
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…
Common noise acting on a population of identical oscillators can synchronize them. We develop a description of this process which is not limited to the states close to synchrony, but provides a global picture of the evolution of the…
We analyze the properties of order parameters measuring synchronization and phase locking in complex oscillator networks. First, we review network order parameters previously introduced and reveal several shortcomings: none of 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 effect of phase-lag parameter in pairwise interactions has been a topic of great interest for long. However, real-world systems often have interactions that are beyond pairwise and can be modeled using simplicial complexes. We…
We analyze star-type networks of phase oscillators by virtue of two methods. For identical oscillators we adopt the Watanabe-Strogatz approach, that gives full an- alytical description of states, rotating with constant frequency. For…
We develop a linear response theory by computing the asymptotic value of the order parameter from the linearized equation of continuity around the nonsynchronized reference state using the Laplace transform in time. The proposed theory is…
Many biological and neural systems can be seen as networks of interacting periodic processes. Importantly, their functionality depends on the emerging collective dynamics of the network. Synchrony of oscillations is one of the most…
We investigate collective synchronization in a system of coupled oscillators on small-world networks. The order parameters which measure synchronization of phases and frequencies are introduced and analyzed by means of dynamic simulations…
We investigate the effect of partial order parameter adaptation in form of general functions on the synchronization behavior of coupled Kuramoto oscillators on top of random hypergraph models. The interactions between the oscillators are…
We study the effects of synchronization and desynchronization in ensembles of phase oscillators with the global Kuramoto-Sakaguchi coupling under common noise driving. Since the mechanisms of synchronization by coupling and by common noise…
We introduce a prototype model for globally-coupled oscillators in which each element is given an oscillation frequency and a preferential oscillation direction (polarization), both randomly distributed. We found two collective transitions:…
The Ott-Antonsen ansatz shows that, for certain classes of distribution of the natural frequencies in systems of $N$ globally coupled Kuramoto oscillators, the dynamics of the order parameter, in the limit $N\to \infty$, evolves, under…
We investigate topological and spectral properties of models of European and US-American power grids and of paradigmatic network models as well as their implications for the synchronization dynamics of phase oscillators with heterogeneous…
We tackle the quantification of synchrony in globally coupled populations. Furthermore, we treat the problem of incomplete observations when the population mean field is unavailable, but only a small subset of units is observed. We…
We consider general properties of groups of interacting oscillators, for which the natural frequencies are not in resonance. Such groups interact via non-oscillating collective variables like the amplitudes of the order parameters defined…
Molecular simulations as well as single molecule experiments have been widely analyzed in terms order parameters, the latter representing candidate probes for the relevant degrees of freedom. Notwithstanding this approach is very intuitive,…