Related papers: Parametric resonance in a conservative system of c…
We introduce a new approach to deriving approximate analytical solutions of a harmonic oscillator damped by purely nonlinear, or combinations of linear and nonlinear damping forces. Our approach is based on choosing a suitable trial…
The effect of multiplicative white noise on the resonance capture in non-isochronous systems with time-decaying pumping is investigated. It is assumed that the intensity of perturbations decays with time, and its frequency is asymptotically…
We develop a theory of parametric excitation of weakly nonlinear standing gravity waves in a tank, which is under vertical vibrations with a slowly time-dependent ("chirped") vibration frequency. We show that, by using a negative chirp, one…
We study the instabilities of a harmonic oscillator subject to additive and dichotomous multiplicative noise, focussing on the dependance of the instability threshold on the mass. For multiplicative noise in the damping, the instability…
We investigate the resonance behaviour in a system composed by n-coupled Duffing oscillators where only the first oscillator is driven by a periodic force, assuming a nearest neighbour coupling. We have derived the frequency-response…
We examine the effects of pure additive noise on spatially extended systems with quadratic nonlinearities. We develop a general multiscale theory for such systems and apply it to the Kuramoto-Sivashinsky equation as a case study. We first…
We describe an opto-mechanical system in which the coupling between optical and mechanical degrees of freedom takes the form of a fully quantised third-order parametric interaction. Two physical realisations are proposed: a harmonically…
Much of the physical world around us can be described in terms of harmonic oscillators in thermodynamic equilibrium. At the same time, the far from equilibrium behavior of oscillators is important in many aspects of modern physics. Here, we…
Nonlinear dynamics plays a significant role in interdisciplinary fields spanning biology, engineering, mathematics, and physics. Under small-amplitude approximations, certain nonlinear systems can be effectively described by the linear…
Coupled, nonlinear oscillators are often studied in applied biology, physics, fluids, and many other disciplines. In this paper, we study a parametrically driven, coupled oscillator system where the individual oscillators are subjected to…
We develop from first principles the coupled wave equations that describe polarization-sensitive parametric amplification based on four-wave mixing in standard (randomly birefringent) optical fibers. We show that in the small-signal case…
In this paper, an attempt has been made to understand the parametric excitation of a periodic orbit of nonlinear oscillator which can be a limit cycle, center or a slowly decaying center-type oscillation. For this a delay model is…
Interferometric gravitational wave detectors operate with high optical power in their arms in order to achieve high shot-noise limited strain sensitivity. A significant limitation to increasing the optical power is the phenomenon of…
This paper investigates the dynamic stability of an electromagnetically suspended vehicle, encountered in Hyperloop and Maglev systems, subject to periodic excitations caused by surface irregularities or vibration of the support induced by…
We discuss the concept of characteristic squeezing modes applied to a travelling-wave optical parametric amplifier pumped by an ultrashort pulse. The characteristic modes undergo decoupled single-mode squeezing transformations, and…
It is shown, that retardation in the $\alpha$-quenching in the Parker's dynamo model leads to parametric resonance. This result is observed in the numerical simulations and can be reproduced in the simple analytic model. The other…
A mathematical model describing the initial stage of the capture into the parametric autoresonance in nonlinear oscillating systems with a dissipation is considered. Solutions with unboundedly growing energy in time at infinity are…
Linear parametric amplification is a key operation in information processing. Our interest here is quantum-limited parametric amplification, $i.e.$, amplification of quantum signals while adding the minimum amount of noise allowed by…
In this work, we investigate the period doubling phenomenon in the periodically forced asymmetric Duffing oscillator. We use the known steady-state asymptotic solution -- the amplitude-frequency implicit function -- and known criterion for…
Asymmetric Ising model, in which coupled spins affect each other differently, plays an important role in diverse fields, from physics to biology to artificial intelligence. We show that coupled parametric oscillators provide a…