Related papers: Resonance of bounded isochronous oscillators
An oscillatory system can have clockwise and anticlockwise senses of rotation. We propose a general rule how to obtain counter-rotating oscillators from the definition of a dynamical system and then investigate synchronization. A type of…
Synchronization in oscillatory systems is a frequent natural phenomenon and is becoming an important concept in modern physics. Nanomechanical resonators are ideal systems for studying synchronization due to their controllable oscillation…
We consider a damped impact oscillator subject to the action of a biharmonic force. The conditions for the existence and stability of almost periodic resonance solutions are investigated.
A time-dependent unitary (canonical) transformation is found which maps the Hamiltonian for a harmonic oscillator with time-dependent real mass and real frequency to that of a generalized harmonic oscillator with time-dependent real mass…
For an attracting periodic orbit (limit cycle) of a deterministic dynamical system, one defines the isochron for each point of the orbit as the cross-section with fixed return time under the flow. Equivalently, isochrons can be…
Two oscillators coupled to a two-level system which in turn is coupled to an infinite number of oscillators (reservoir) are considered, bringing to light the occurrence of synchronization. A detailed analysis clarifies the physical…
Rotating black holes can produce superradiant clouds of ultralight bosons. When the black hole is part of a binary system, its cloud can undergo resonances and ionization. These processes leave a distinct signature on the gravitational…
We study the synchronization phenomena in a system of globally coupled oscillators with time delay in the coupling. The self-consistency equations for the order parameter are derived, which depend explicitly on the amount of delay. Analysis…
Coherent resonance is the effect of resonant excitation of nonlinear coherent modes in trapped Bose condensates. This novel effect is shown to be feasible for Bose-condensed trapped gases. Conditions for realizing this effect are derived. A…
For system of two ordinary differential equations of the second order representing autonomous non-conservative holonomic mechanical system, in case of dynamics such as one-frequency periodical oscillations, is found integrated invariant of…
Inverse stochastic resonance comprises a nonlinear response of an oscillatory system to noise where the frequency of noise-perturbed oscillations becomes minimal at an intermediate noise level. We demonstrate two generic scenarios for…
Summary: A system of autonomous ordinary differential equations depending on a small parameter is considered such that the unperturbed system has an invariant manifold of periodic solutions that is not normally hyperbolic but is normally…
We consider the phenomenon of mutual synchronization in a fundamental quantum system of two detuned quantum harmonic oscillators dissipating into the environment. We identify the conditions leading to this spontaneous phenomenon showing…
We consider one-dimensional systems in the presence of a quasi-periodic perturbation, in the analytical setting, and study the problem of existence of quasi-periodic solutions which are resonant with the frequency vector of the…
Shared upstream dynamical processes are frequently the source of common inputs in various physical and biological systems. However, due to finite signal transmission speeds and differences in the distance to the source, time shifts between…
The mechanism of phase synchronization between uncoupled limit-cycle oscillators induced by common external impulsive forcing is analyzed. By reducing the dynamics of the oscillator to a random phase map, it is shown that phase…
Some of the most enduring questions in physics--including the quantum measurement problem and the quantization of gravity--involve the interaction of a quantum system with a classical environment. Two linearly coupled harmonic oscillators…
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…
In this paper a procedure is described which allows to identify new systems of nonlinear recursions whose solutions are controllable and which may be asymptotically isochronous as functions of the independent variable (considered a ticking…
It was usually assumed that the resonator based on a waveguide has the eigen oscillations that are formed by interference of two waves which propagate in different directions and have equal amplitudes. These patterns are usually called…