Related papers: Analyzing Oscillators using Describing Functions
We investigate symmetric oscillators, and in particular their quantization, by employing semiclassical and quantum phase functions introduced in the context of Liouville-Green transformations of the Schr\"{o}dinger equation. For anharmonic…
The phase reduction technique is essential for studying rhythmic phenomena across various scientific fields. It allows the complex dynamics of high-dimensional oscillatory systems to be expressed by a single phase variable. This paper…
Characteristic functions are shown to be useful for highly sensitive measurements. Redistributions of motional Fock states of a trapped atom can be directly monitored via the most fragile nonclassical part of the characteristic function.…
The problem of determining the mathematical model of the dynamics of multi-dimensional control systems in the presence of noise under the condition that the correlation functions cannot be found. Known statistical dynamics of linear systems…
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,…
Nonlinearity is a central feature in demanding computing applications that aim to deal with tasks such as optimization or classification. Furthermore, the consensus is that nonlinearity should not be only exploited at the algorithm level,…
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…
This work is a theoretical investigation of the stability of the non-linear behavior of an oscillating tip-cantilever system used in dynamic force microscopy. Stability criterions are derived that may help to a better understanding of the…
As known all physical properties of solids are described well by the system of quantum linear harmonic oscillators. It is shown in the present paper that the system consisting of classical linear harmonic oscillators having temperature…
Linear time invariant (LTI) systems are widely used for modeling system dynamics in science and engineering problems. Harmonic oscillation of LTI systems are widely used for modeling and analyses of periodic physical phenomenon. This study…
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…
Differentiable simulators continue to push the state of the art across a range of domains including computational physics, robotics, and machine learning. Their main value is the ability to compute gradients of physical processes, which…
This paper presents comprehensive studies on frequency response optimized integrators considering second order derivative regarding their numerical error, numerical stability and transient performance. Frequency domain error analysis is…
Determining functionals are tools to describe the finite dimensional long-term dynamics of infinite dimensional dynamical systems. There also exist several applications to infinite dimensional {\em random} dynamical systems. In these…
We propose a method for designing two-dimensional limit-cycle oscillators with prescribed periodic trajectories and phase response properties based on the phase reduction theory, which gives a concise description of weakly-perturbed…
Nonlinear elastic effects play an important role in the dynamics of microelectromechanical systems (MEMS). Duffing oscillator is widely used as an archetypical model of mechanical resonators with nonlinear elastic behavior. In contrast,…
For noisy self-sustained oscillators, both reliability, stability of a response to a noisy driving, and coherence understood in the sense of constancy of oscillation frequency belong to the main characteristics. Though the both…
The stability analysis of elastic rings subjected to various loading conditions is examined, focusing on stable and unstable configurations. The harmonic balance method is employed to investigate the stability range under different loading…
Self-sustaining nonlinear oscillators of practically any type can function as latches and registers if Boolean logic states are represented physically as the phase of oscillatory signals. Combinational operations on such phase-encoded logic…
We present a simple algorithm for detecting oscillatory behavior in discrete data. The data is used as an input driving force acting on a set of simulated damped oscillators. By monitoring the energy of the simulated oscillators, we can…