Related papers: An efficient method for approximating resonance cu…
Employing both Bayesian statistics and the theory of nonlinear dynamics, we present a practically efficient method to extract a phase description of weakly coupled limit-cycle oscillators directly from time series observed in a rhythmic…
Nonlinear spin dynamics are essential in exploring nonequilibrium quantum phenomena and have broad applications in precision measurement. Among these systems, the combination of a bias magnetic field and feedback mechanisms can induce…
Mechanical nonlinearities dominate the motion of nanoresonators already at relatively small oscillation amplitudes. Although single and coupled two-degrees-of-freedom models have been used to account for experimentally observed nonlinear…
We study resonances of nonlinear systems of differential equations, including but not limited to the equations of motion of a particle moving in a potential. We use the calculus of variations to determine the minimal additive forcing…
The harmonic balance (HB) method is widely used in the literature for analyzing the periodic solutions of nonlinear mechanical systems. The objective of this paper is to exploit the method for bifurcation analysis, i.e., for the detection…
We consider frequency fluctuations in self-sustained oscillators based on nonlinear underdamped resonators. An important type of such resonators are nano- and micro-electro-mechanical systems. Various noise sources are considered, with the…
Multi-frequency forcing of systems undergoing a Hopf bifurcation to spatially homogeneous oscillations is investigated using a complex Ginzburg-Landau equation that systematically captures weak forcing functions that simultaneously hit the…
A nonlinear frequency response based adaptive vibration controller is proposed for a class of nonlinear mechanical systems. In order to obtain the nonlinear Frequency Response Function (FRF), the convergence properties of the system are…
We develop a moment equation closure minimization method for the inexpensive approximation of the steady state statistical structure of nonlinear systems whose potential functions have bimodal shapes and which are subjected to correlated…
A quantum harmonic oscillator (spring subsystem) is stabilized towards a target Fock state by reservoir engineering. This passive and open-loop stabilization works by consecutive and identical Hamiltonian interactions with auxiliary…
We show how spectral submanifold theory can be used to construct reduced-order models for harmonically excited mechanical systems with internal resonances. Efficient calculations of periodic and quasi-periodic responses with 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…
This article describes a method for constructing approximations to periodic solutions of dynamic Lorenz system with classical values of the system parameters. The author obtained a system of nonlinear algebraic equations in general form…
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 content of this contribution is based on the course on numerical analysis techniques for non-linear dynamics. After introducing basic concepts as the visual analysis of trajectories in phase space and the importance of the nature of…
Forced oscillation event in power grids refers to a state where malfunctioning or abnormally operating equipment causes persisting periodic disturbances in the system. While power grids are designed to damp most of perturbations during…
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 investigate the dynamics of mechanical resonators subject to excitations comprising of an oscillating or harmonic part, whose amplitude decays exponentially in time. We call these complex frequency excitations and show that the resulting…
Driven non-linear resonators can display sharp resonances or even multistable behaviours amenable to induce strong enhancements of weak signals. Such enhancements can make use of the phenomenon of vibrational resonance whereby a weak…
Energy distributions of high frequency linear wave fields are often modelled in terms of flow or transport equations with ray dynamics given by a Hamiltonian vector field in phase space. Applications arise in underwater and room acoustics,…