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We compare the Gram-Schmidt and covariant phase-space-basis-vector descriptions for three time-reversible harmonic oscillator problems, in two, three, and four phase-space dimensions respectively. The two-dimensional problem can be solved…

We consider one-dimensional chains and multi-dimensional networks of harmonic oscillators coupled to two Langevin heat reservoirs at different temperatures. Each particle interacts with its nearest neighbors by harmonic potentials and all…

We demonstrate that a system of nonlocally coupled noisy phase oscillators can collectively exhibit a hole structure, which manifests itself in the spatial phase distribution of the oscillators. The phase model is described by a nonlinear…

We investigate phase-locked solutions of a continuum field of nonlocally coupled identical phase oscillators with distance-dependent propagation delays. Equilibrium relations for both synchronous and traveling wave solutions in the…

We consider a system of coupled oscillators with finite inertia and time-delayed interaction, and investigate the interplay between inertia and delay both analytically and numerically. The phase velocity of the system is examined; revealed…

In this paper we study a system of $N$ coupled quantum oscillators interacting with each other directly with varying coupling strengths and indirectly through linear couplings to a scalar massless quantum field as its environment. The…

Acoustics recently became a versatile platform for discovering novel physical effects and concepts at a relatively simple technological level. On this way, single resonators and the structure of their resonant modes play a central role and…

Many systems of physical and biological interest are characterized by assemblies of phase oscillators whose interaction is mediated by a diffusing chemical. The coupling effect results from the fact that the local concentration of the…

Twin beam fluctuations are analyzed for detuned and mismatched OPO configurations. Resonances and frequency responses to the quantum noise sources (quantum and pump amplitude/phase fluctuations) are examined as functions of cavity decay…

We consider a Hamiltonian system of coupled Van der Pol-Duffing(VdPD) oscillators with balanced loss and gain. The system is analyzed perturbatively by using Renormalization Group(RG) techniques as well as Multiple Scale Analysis(MSA). Both…

We address two aspects of the dynamics of the forced Duffing oscillator which are relevant to the technology of micromechanical devices and, at the same time, have intrinsic significance to the field of nonlinear oscillating systems. First,…

In this paper we present a comprehensive analysis of the coherence phenomenon of two coupled dissipative oscillators. The action of a classical driving field on one of the oscillators is also analyzed. Master equations are derived for both…

We study the Wigner function of phase-locked nondegenerate optical parametric oscillator and find the signatures of both phase-locking and self-pulsing phenomena in phase space. We also analyze the problem of continuous-variable…

Spontaneous synchronization between coupled periodic systems occur in a wealth of classical physical setups. Here, we show theoretically that the phase of two distinct quantum harmonic oscillators spontaneously when they are strongly…

Synchronization is a hallmark of collective behavior that emerges when nonlinear systems interact, spanning scales from mechanical oscillators to planetary orbits. As a universal phenomenon it underpins the study of complex systems and has…

The new phenomenological model of the ensemble of three neurons with chemical (synaptic) and electrical couplings has been studied. One neuron is modeled by a single Van der Pol oscillator. The influence of the electrical coupling strength…

The synchronization stability of a complex network system of coupled phase oscillators is discussed. In case the network is affected by disturbances, a stochastic linearized system of the coupled phase oscillators may be used to determine…

We study the response of an ensemble of synchronized phase oscillators to an external harmonic perturbation applied to one of the oscillators. Our main goal is to relate the propagation of the perturbation signal to the structure of the…

We investigate the existence and stability of travelling wave solutions in a continuum field of non-locally coupled identical phase oscillators with distance-dependent propagation delays. A comprehensive stability diagram in the parametric…

We consider an ensemble of globally coupled phase oscillators whose interaction is transmitted at finite speed. This introduces time delays, which make the spatial coordinates relevant in spite of the infinite range of the interaction. We…