Related papers: On the Collective Behavior of Parametric Oscillato…
We investigate emergence of the global collective behavior in networks of diffusively coupled identical oscillators, which in the established model is an invariant manifold of the motion equations. The interaction is modeled with the graph…
An ensemble of pulse-coupled phase-oscillators is thoroughly analysed in the presence of a mean-field coupling and a dispersion of their natural frequencies. In spite of the analogies with the Kuramoto setup, a much richer scenario is…
We study the phase synchronization between collective rhythms of fully locked oscillator groups. For weakly interacting groups of two oscillators with global sinusoidal coupling, we analytically derive the collective phase coupling…
Coupled parametric oscillators were recently employed as simulators of artificial Ising networks, with the potential to solve computationally hard minimization problems. We demonstrate a new dynamical regime within the simplest network -…
Many real systems comprised of a large number of interacting components, as for instance neural networks , may exhibit collective periodic behavior even though single components have no natural tendency to behave periodically. Macroscopic…
Oscillator networks with an asymmetric bipolar distribution of natural frequencies are useful representations of power grids. We propose a mean-field model that captures the onset, form and linear stability of frequency synchronization in…
The parameterization method (PM) provides a broad theoretical and numerical foundation for computing invariant manifolds of dynamical systems. PM implements a change of variables in order to represent trajectories of a system of ordinary…
We examine kinematic dynamo action driven by an axisymmetric large scale flow that is superimposed with an azimuthally propagating non-axisymmetric perturbation with a frequency $\omega$. Although we apply a rather simple large scale…
We analyze a simple stochastic model to describe motor molecules which cooperate in large groups and present a physical mechanism which can lead to oscillatory motion if the motors are elastically coupled to their environment. Beyond a…
A model for synchronization of globally coupled phase oscillators including ``inertial'' effects is analyzed. In such a model, both oscillator frequencies and phases evolve in time. Stationary solutions include incoherent (unsynchronized)…
Phase synchronization between collective oscillations exhibited by two weakly interacting groups of non-identical phase oscillators with internal and external global sinusoidal coupling of the groups is analyzed theoretically. Coupled…
We study the synchronization phenomena in a system of globally coupled oscillators with time delay in the coupling. The self-consistency equations for the order parameter are derived, which depend explicitly on the amount of delay. Analysis…
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…
Phase-coupled oscillators serve as paradigmatic models of networks of weakly interacting oscillatory units in physics and biology. The order parameter which quantifies synchronization was so far found to be chaotic only in systems with…
We derive simple conditions for the stability or instability of the synchronized oscillation of a class of networks of coupled phase-oscillators, which includes many of the systems used in neural modelling.
Mixtures of near-symmetric oppositely charged components with strong attractive short range interactions exhibit ordered lamellar phases at low temperatures. In the strong segregation limit the state of these systems can be described by the…
We study the properties of large systems of globally coupled oscillators in the presence of noise. When the distribution of the natural frequencies of the oscillators is bimodal and its analytical continuation in the complex plane has only…
The collective behavior in a population of globally coupled oscillators with randomly distributed frequencies is studied when the natural frequency distribution does not possess an even symmetry with respect to the average natural frequency…
We investigate parametric resonance in oscillator networks subjected to periodically time-varying oscillations in the edge strengths. Such models are inspired by the well-known parametric resonance phenomena for single oscillators, as well…
We consider a model where a population of diffusively coupled limit-cycle oscillators, described by the complex Ginzburg-Landau equation, interacts nonlocally via an inertial field. For sufficiently high intensity of nonlocal inertial…