Related papers: Nonlinear Dynamics and Chaos in Two Coupled Nanome…
As a model of coupled nano-electromechanical resonantors we study two nonlinear driven oscillators with an arbitrary coupling strength between them. Analytical expressions are derived for the oscillation amplitudes as a function of the…
The oscillatory response of nonlinear systems exhibits characteristic phenomena such as multistability, discontinuous jumps and hysteresis. These can be utilized in applications leading, e.g., to precise frequency measurement, mixing,…
We demonstrate a system composed of two resonators that are coupled solely through a nonlinear interaction, and where the linear properties of each resonator can be controlled locally. We show that this class of dynamical systems has…
Nanomechanical resonators, machined out of Silicon-on-Insulator wafers, are operated in the nonlinear regime to investigate higher-order mechanical mixing at radio frequencies, relevant to signal processing and nonlinear dynamics on…
We consider chaotic dynamics of a system of two coupled ring resonators with a linear gain and a nonlinear absorption. Such a structure can be implemented in various settings including microresonator nanostructures, polariton condensates,…
Many nonlinear systems are described by eigenmodes with amplitude-dependent frequencies, interacting strongly whenever the frequencies become commensurate at internal resonances. Fast energy exchange via the resonances holds the key to rich…
The dynamics of nanomechanical resonators driven by both low- and high-frequency signals is studied. Considering, as an example, resonators made of a doubly-clamped beam with magnetomotive driving, it is shown that three-frequency…
We investigate theoretically the non-linear dynamics of a coupled nanomechanical oscillator. Under a weak radio frequency excitation, the resonators can be parametrically tuned into a self-sustained oscillatory regime. The transfer of…
Chaotic systems, presenting complex and non-reproducible dynamics, may be found in nature from the interaction between planets to the evolution of the weather, but can also be tailored using current technologies for advanced signal…
Controlling nonlinear effects in micro- and nano-electro-mechanical systems is essential for unlocking their full potential in sensing, signal processing, and frequency control. In this study, we develop a voltage-dependent Hamiltonian…
We study nonlinear resonance of coupled modes in nano-mechanical systems. To reveal the qualitative features of the dynamics, we consider the limiting cases, where the results can be obtained analytically. For 1:3 resonance, we find the…
A nonlinear oscillator with an abruptly inhomogeneous restoring force driven by an uniform oscillating force exhibits stochastic properties under specific resonance conditions. This behaviour elucidates the elementary mechanism of the…
Coupling, synchronization, and non-linear dynamics of resonator modes are omnipresent in nature and highly relevant for a multitude of applications ranging from lasers to Josephson arrays and spin torque oscillators. Nanomechanical…
We analyze stability of a system which contains an harmonic oscillator non-linearly coupled to its second harmonic, in the presence of a driving force. It is found that there always exists a critical amplitude of the driving force above…
The study of collective nonlinear dynamics of coupled mechanical resonators is regaining attention in recent years thanks to rapid developments in the fields of microelectromechanical and nanoelectromechanical systems (MEMS and NEMS). We…
A nonlinear two-dimensional system is studied by making use of both the Lagrangian and the Hamiltonian formalisms. The present model is obtained as a two-dimensional version of a one-dimensional oscillator previously studied at the…
We propose an anharmonic oscillator driven by two periodic forces of different frequencies as a new time-dependent model for investigating quantum dissipative chaos. Our analysis is done in the frame of statistical ensemble of quantum…
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…
We investigate the coupled-system dynamics of two-level quantum dots placed on a vibrating nanomechanical resonator. The ensemble of quantum dots exhibits superradiance features which are transferred to the mechanical degrees of freedom…
We present initial results regarding the existence, stability and interaction of linear and nonlinear vibrational modes in a system of two coupled, one dimensional lattices with unequal numbers of masses. The effects on these nonlinear…