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We design, characterize, and couple Boolean phase oscillators that include state-dependent feedback delay. The state-dependent delay allows us to realize an adjustable coupling strength, even though only Boolean signals are exchanged.…
Synchronization is studied in an array of identical oscillators undergoing small vibrations. The overall coupling is described by a pair of matrix-weighted Laplacian matrices; one representing the dissipative, the other the restorative…
The nature of the ground states for a system composed of two coupled cavities with each containing a pair of dipole-coupled two-level atoms are studied over a wide range of detunings and dipole coupling strengths. The cases for three limits…
The particular properties of synchronization are discussed for coupled auto-oscillating systems, which are characterized by non-quadratic law of potential dependence on the coordinate. In particular, structure of the parameter plane…
Here we present a system of coupled phase oscillators with nearest neighbors coupling, which we study for different boundary conditions. We concentrate at the transition to total synchronization. We are able to develop exact solutions for…
We consider a system of three interacting van der Pol oscillators with reactive coupling. Phase equations are derived, using proper order of expansion over the coupling parameter. The dynamics of the system is studied by means of the…
We develop an approach to study the entanglement in two coupled harmonic oscillators. We start by introducing an unitary transformation to end up with the solutions of the energy spectrum. These are used to construct the corresponding…
Klauder's recent generalization of the harmonic oscillator coherent states [J. Phys. A 29, L293 (1996)] is applicable only in non-degenerate systems, requiring some additional structure if applied to systems with degeneracies. The author…
We study ground states of two-component condensates in a harmonic trap. We prove that in the strongly coupled and weakly interacting regime, the two components segregate while a symmetry breaking occurs. More precisely, we show that when…
Oscillator networks display intricate synchronization patterns. Determining their stability typically requires incorporating the symmetries of the network coupling. Going beyond analyses that appeal only to a network's automorphism group,…
We investigate globally coupled stochastic three-state oscillators, which we consider as general models of stochastic excitable systems. We compare two situations:in the first case the transitions between the three states of each unit…
This paper describes how the structure of the state space of the quantum harmonic oscillator can be described by an adjunction of categories, that encodes the raising and lowering operators into a commutative comonoid. The formulation is an…
In this work, we perform a careful study of an special arrangement of coupled systems that consists of two external harmonic oscillators weakly coupled to an arbitrary network (data bus) of strongly interacting oscillators. Our aim is to…
Synchronisation between coupled oscillatory systems is a common phenomenon in many natural as well as technical systems. Varying the strength of coupling often leads to qualitative changes in the complex dynamics of the mutually coupled…
There is recent interest in the inter and intra element interactions of metamaterial unit cells. To calculate the effects of these interactions which can be substantial, an ab initio general coupled mode equation, in the form of an…
In networks of identical linear oscillators (e.g. pendulums undergoing small vibrations) coupled through both dissipative connectors (e.g. dampers) and restorative connectors (e.g. springs) the relation between asymptotic synchronization…
We propose the definition of the geometric measure of entanglement for continuous variable states. On the basis of this definition we examine entanglement of the graph states obtained as a result of action of a unitary operator on the…
Synchronization of identical harmonic oscillators interconnected via position, velocity, and acceleration couplings is studied. How to construct a complex Laplacian matrix representing the overall coupling is presented. It is shown that the…
We investigate coupled identical phase oscillators with scale-free distribution of coupling strength. It is shown that partially locked states can occur due to the inhomogeneity in coupling and some properties of the coupling function.…
We consider networks of coupled stochastic oscillators. When coupled we find strong collective oscillations, while each unit remains stochastic. In the limit (N\to \infty) we derive a system of integro-delay equations and show analytically…