Related papers: Oscillators with Parametrically Excited Nonlineari…
We consider the properties of the small-signal modulation response of symmetry-breaking phase-locked states of twin coupled semiconductor lasers. The extended stability and the varying asymmetry of these modes allows for the introduction of…
We construct nonlinear squeezed states of a generalized isotonic oscillator potential. We demonstrate the non-existence of dual counterpart of nonlinear squeezed states in this system. We investigate statistical properties exhibited by the…
Frequency entrainment of continuous-variable oscillators has to date been restrained to the weakly nonlinear regime. Here we overcome this bottleneck and extend frequency entrainment of quantum continuous-variable oscillators to arbitrary…
The response of a coupled array of nonlinear oscillators to parametric excitation is calculated in the weak nonlinear limit using secular perturbation theory. Exact results for small arrays of oscillators are used to guide the analysis of…
The properties of the three-dimensional noncanonical osp(3/2) oscillators, introduced in J.Phys. A: Math. Gen. {\bf 27} (1994) 977, are further studied. The angular momentum M of the oscillators can take at most three values M=p-1,p,p+1,…
We explore the spectral properties and behaviour of confining superexponential potentials. Several prototypes of these highly nonlinear potentials are analyzed in terms of the eigenvalues and eigenstates of the underlying stationary…
Phase transitions and the associated symmetry breaking are at the heart of many physical phenomena. Coupled systems with multiple interacting degrees of freedom provide a fertile ground for emergent dynamics that is otherwise inaccessible…
We introduce a new method for reducing phase noise in oscillators, thereby improving their frequency precision. The noise reduction device consists of a pair of coupled nonlinear resonating elements that are driven parametrically by the…
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…
We propose a scheme for obtaining highly-sensitive oscillators in a coupled-resonator system with an exceptional point of degeneracy (EPD) and a small instability. The oscillator with the exceptional degeneracy is realized by using two…
The model of a double-well oscillator with nonlinear dissipation is studied. The self-sustained oscillations regime and the excitable one are described. The first regime consists in the coexistence of two stable limit cycles in the phase…
Motivated by recent experiments, where a voltage biased Josephson junction is placed in series with a resonator, the classical dynamics of the circuit is studied in various domains of parameter space. This problem can be mapped onto the…
We present a time-dependent quantum calculation of the van der Waals interaction between a pair of dissimilar atoms, one of which is initially excited while the other one is in its ground state. For small detuning, the interaction is…
The Duffing oscillator is a nonlinear extension of the ubiquitous harmonic oscillator and as such plays an outstanding role in science and technology. Experimentally, the system parameters are determined by a measurement of its response to…
We study the synchronization of dissipatively-coupled van der Pol oscillators in the quantum limit, when each oscillator is near its quantum ground state. Two quantum oscillators with different frequencies exhibit an entanglement tongue,…
We demonstrate the deterministic coherence and anti-coherence resonance phenomena in two coupled identical chaotic Lorenz oscillators. Both effects are found to occur simultaneously when varying the coupling strength. In particular, the…
We present approximate analytical method of analysis of stationary states of nonlinear quantum systems with the noise. As an example we consider quantum nonlinear oscillator excited by fluctuating force and found parameter regions with more…
Nonlinear isolated and coupled oscillators are extensively studied as prototypical nonlinear dynamics models. Much attention has been devoted to oscillator synchronization or the lack thereof. Here, we study the synchronization and…
A classical linear oscillator is treated in the small amplitude limit so that it will be approximately relativistic. The oscillator involves a charge particle in a linear potential in classical zero-point radiation. It is found that the…
A mathematical model describing the initial stage of the capture into autoresonance for nonlinear oscillating systems with combined parametric and external excitation is considered. The solutions with unboundedly growing amplitude and…