Related papers: Three-frequency resonances in dynamical systems
The ability to approach a physical phenomenon and grasp its major importance is a remarkable quality of understanding. This paper presents a rather elegant and novel way of looking at the resonance phenomenon, which among others shares a…
This work explores the dynamic properties of test particles surrounding a distorted, deformed compact object. The astrophysical motivation was to choose such background, which could constitute a more reasonable model of a real situation…
In this paper, we consider the problem of mechanical wave scattering from a spatially finite system into an infinite surrounding environment. The goal is to illuminate why the scattering spectrum undergoes peaks and dips (resonances) at…
One unusual property of dynamic systems, whose state is characterized by a set of scalar dynamic variables satisfying a system of differential equations of a general form, is considered. This property is related to the behavior of equations…
The complex scaling method permits calculations of few-body resonances with the correct asymptotic behaviour using a simple box boundary condition at a sufficiently large distance. This is also valid for systems involving more than one…
The influence of out-of-plane oscillations on friction is a well-known phenomenon that has been studied extensively with various experimental methods, e.g. pin-on-disk tribometers. However, existing theoretical models have yet achieved only…
We present a new chaotic system of three coupled ordinary differential equations, limited to quadratic nonlinear terms. A wide variety of dynamical regimes are reported. For some parameters, chaotic reversals of the amplitudes are produced…
Dynamical decoupling techniques constitute an integral part of many quantum sensing platforms, often leading to orders-of-magnitude improvements in coherence time and sensitivity. Most AC sensing sequences involve a periodic echo-like…
Dissipative phenomena manifest in multiple mechanical systems. In this dissertation, different geometric frameworks for modelling non-conservative dynamics are considered. The objective is to generalize several results from conservative…
We show that it is possible for chaotic systems to display the main features of coherence resonance. In particular, we show that a Chua model, operating in a chaotic regime and in the presence of noise, can exhibit oscillations whose…
Dynamical maps describe general transformations of the state of a physical system, and their iteration can be interpreted as generating a discrete time evolution. Prime examples include classical nonlinear systems undergoing transitions to…
Model optomechanical systems with photon-vibration interactions linear, quadratic, and cubic in mechanical displacements are studied under conditions for adiabatic elimination of the photon field. The opportunity of transformation of…
This paper is a preliminary work to address the problem of dynamical systems with parameters varying in time. An idea to predict their behaviour is proposed. These systems are called \emph{transient systems}, and are distinguished from…
We present a simple and unified classification of macroscopic electromagnetic resonances in finite arbitrarily inhomogeneous isotropic dielectric 3D structures situated in free space. By observing the complex-plane dynamics of the spatial…
Two different "wave chaotic" systems, involving complex eigenvalues or resonances, can be analyzed using common semiclassical methods. In particular, one obtains fractal Weyl upper bounds for the density of resonances/eigenvalues near the…
Stability is a key property of dynamical systems. In some cases, we want to change unstable system into stable one to achieve certain goals in engineering. Here, we present an example of a $3$ dimensional switched system that alternates…
We study the dynamical behaviors of a system of five coupled nonlinear equations that describes the dynamics of acoustic-gravity waves in the atmosphere. A linear stability analysis together with the analysis of Lyapunov exponents spectra…
Studying the dynamical behavior of micro- and nano-mechanical systems (MEMS and NEMS) is essential in various fields from nonlinear dynamics to quantum technologies. Hence, it is important to be able to precisely monitor the mechanical…
A genuinely three-dimensional system, viz. the hyperbolic 4-sphere scattering system, is investigated with classical, semiclassical, and quantum mechanical methods at various center-to-center separations of the spheres. The efficiency and…
In propagating wave systems, three or four-wave resonant interactions constitute a classical non-linear mechanism exchanging energy between the different scales. Here we investigate three-wave interactions for gravity-capillary surface…