Related papers: Phase resonance nonlinear modes of mechanical syst…
Nonlinear dynamical systems possessing reflection symmetry have an invariant subspace in the phase space. The dynamics within the invariant subspace can be random or chaotic. As a system parameter changes, the motion transverse to the…
The parameterization method (PM) provides a broad theoretical and numerical foundation for computing invariant manifolds of dynamical systems. PM implements a change of variables in order to represent trajectories of a system of ordinary…
We investigate in this paper the superharmonic and subharmonic resonances of forced modified Rayleigh-Duffing oscillator. We analyse this equation by the method of multiple scales and we obtain superharmonic, subharmonic resonances…
In this work, we investigate the gravitational quasinormal modes (QNMs) and the gravitational resonances of a thick brane model. We use the asymptotic iteration and shooting methods to obtain the quasinormal frequencies (QNFs) of the brane.…
This book chapter describes the dynamics of a modulated oscillator for resonant and nonresonant modulation. Two types of resonant modulation are considered: additive, with frequency close to the oscillator eigenfrequency, and parametric,…
We examine the time-dependent behavior of a nonlinear system driven by a two-frequency forcing. By using a non-perturbative approach, we are able to derive an asymptotic expression, valid in the long-time limit, for the time average of the…
We investigate the sideband spectra of a driven nonlinear mode with its eigenfrequency being modulated at a low frequency (< 1 kHz). This additional parametric modulation leads to prominent antiresonance lineshapes in the sideband spectra,…
A dual-excitation method for resonant-frequency tracking in scanning probe microscopy based on amplitude detection is developed. This method allows the cantilever to be operated at or near resonance for techniques where standard phase…
Synchronization has been reported for a wide range of self-oscillating systems. However, even though it has been predicted theoretically for several decades, the experimental realization of phase self-oscillation, sometimes called phase…
We analyze the dynamics of a two-level system subject to driving by large-amplitude external fields, focusing on the resonance properties in the case of driving around the region of avoided level crossing. In particular, we consider three…
We introduce the concept of phase-synchronous undersampling in nonlinear spectroscopy. The respective theory is presented and validated experimentally in a phase-modulated quantum beat experiment by sampling high phase modulation…
The combined influence of oscillatory excitations and multiplicative stochastic perturbations of white noise type on isochronous systems in the plane is investigated. It is assumed that the intensity of perturbations decays with time and…
Self-sustained vibrations in systems ranging from lasers to clocks to biological systems are often associated with the coefficient of linear friction, which relates the friction force to the velocity, becoming negative [1,2]. The runaway of…
This paper develops a harmonic-domain framework for systems with variable fundamental frequency. A variable-frequency sliding Fourier decomposition is introduced in the phase domain, together with necessary and sufficient conditions for…
Linear response spectra of a driven intrinsic localized mode in a micromechanical array are measured as it approaches two fundamentally different kinds of bifurcation points. A linear phase mode associated with this autoresonant state…
Nonlinear phononics has emerged as a powerful paradigm for the nonthermal control of quantum materials by engineering a conservative potential energy landscape. Here, we show that dissipation can serve as an additional control knob for…
The role of phase in neural sequence models remains poorly understood. To isolate this question, we introduce PRISM, a complex-valued encoder that enforces a unit-norm constraint ($|z| = 1$) and replaces attention with gated spectral…
Bestriding the realms of classical and quantum mechanics, nanomechanical structures offer great promise for a huge variety of applications, from computer memory elements \cite{badzey04} and ultra-fast sensors to quantum computing.…
Femtosecond optical pulses at mid-infrared frequencies have opened up the nonlinear control of lattice vibrations in solids. So far, all applications have relied on second order phonon nonlinearities, which are dominant at field strengths…
In Part I of this paper, we have used spectral submanifold (SSM) theory to construct reduced-order models for harmonically excited mechanical systems with internal resonances. In that setting, extracting forced response curves formed by…