Related papers: Stability of the self-phase-locked pump-enhanced s…
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 study the formation of gap solitons in the presence of parametric pump. It is shown that parametric pump can stabilize stationary solitons continuously emitting dispersive waves. The resonant interactions of the radiation and the…
Time-decaying perturbations of nonlinear oscillatory systems in the plane are considered. It is assumed that the unperturbed systems are non-isochronous and the perturbations oscillate with an asymptotically constant frequency. Resonance…
Polarisation effects in the microcavity parametric oscillator are studied using a simple model in which two chi-three optical parametric oscillators are coupled together. It is found that there are, in general, a number of steady states of…
Classical and quantum dynamics of a harmonic oscillator in a monochromatic wave is studied in the exact resonance and near resonance cases. This model describes, in particular, a dynamics of a cold ion trapped in a linear ion trap and…
The steady state in three-level lambda and ladder systems is studied. It is well-known that in a lambda system this steady state is the coherent population trapping state, independent of the presence of spontaneous emission. In contrast,…
We theoretically study the frequency stability of an opto-mechanical radio frequency oscillator based on resonant interaction of two optical and one mechanical modes of the same optical microcavity. A generalized expression for the phase…
We investigate the stability of the synchronization manifold in a ring and an open-ended chain of nearest neighbors coupled self-sustained systems, each self-sustained system consisting of multi-limit cycles van der Pol oscillators. Such…
We study optomechanical interactions in non-Hermitian photonic molecules that support two photonic states and one acoustic mode. The nonlinear steady-state solutions and their linear stability landscapes are investigated as a function of…
We consider an array of nearest-neighbor coupled nonlinear autonomous oscillators with quenched random frequencies and purely conservative coupling. We show that global phase-locked states emerge in finite lattices and study numerically…
For general networks of pulse-coupled oscillators, including regular, random, and more complex networks, we develop an exact stability analysis of synchronous states. As opposed to conventional stability analysis, here stability is…
A class of asymptotically autonomous systems on the plane with oscillatory coefficients is considered. It is assumed that the limiting system is Hamiltonian with a stable equilibrium. The effect of damped multiplicative stochastic…
Phase-locked solutions of coupled oscillators are studied with asymmetric coupling strengths or inhomogeneous natural frequencies. The solutions show remarkable profiles of phase lags from the pacemaker corresponding to the ratio of upward…
Cooperative effects in oscillator networks are often associated with enhanced stability of phase-locked solutions, which increases with system size. We show that the stabilization of persistent currents in annular atomic superfluids with…
We consider the resonant system of amplitude equations for the conformally invariant cubic wave equation on the three-sphere. Using the local bifurcation theory, we characterize all stationary states that bifurcate from the first two…
In this article we study synchronization of systems of homogeneous phase-coupled oscillators with plastic coupling strengths and arbitrary underlying topology. The dynamics of the coupling strength between two oscillators is governed by the…
Coupled semiconductor lasers are systems possessing complex dynamics that are interesting for numerous applications in photonics. In this work, we investigate the existence and the stability of asymmetric phase-locked states of the…
The paper describes a novel parametric excitation scheme that acts as a tunable amplifier by controlling two pumping signals and two nonlinear feedback terms. By modulating the stiffness of a mechanical oscillator with a digital signal…
A hallmark of mechanical resonators made from a single nanotube is that the resonance frequency can be widely tuned. Here, we take advantage of this property to realize parametric amplification and self-oscillation. The gain of the…
We experimentally investigate the dynamic instability of Bose-Einstein condensates in an optical ring resonator that is asymmetrically pumped in both directions. We find that, beyond a critical resonator-pump detuning, the system becomes…