Related papers: Nonlinear Dynamics and Chaos in Two Coupled Nanome…
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.…
Investigating the possibility of applying techniques from linear systems theory to the setting of nonlinear systems has been the focus of many papers. The pseudo linear form representation of nonlinear dynamical systems has led to the…
The classical and quantum dynamics of two ultra-strongly coupled and weakly nonlinear resonators cannot be explained using the Discrete Nonlinear Schr\"odinger Equation or the Bose-Hubbard model, respectively. Instead, a model beyond the…
Synchronization and chaos are two well known and ubiquitous phenomena in nature. Interestingly, under specific conditions, coupled chaotic systems can display synchronization in some of their observables. Here, we experimentally investigate…
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,…
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 show the possibility of controlling the dynamical behavior of a single fiber ring (SFR) resonator system with the fiber being an amplified (gain) channel and the ring being attenuated (loss) nonlinear dielectric medium. Our model is…
Characterizing the emergence of chaotic dynamics of complex networks is an essential task in nonlinear science with potential important applications in many fields such as neural control engineering, microgrid technologies, and ecological…
We investigate an oscillator linearly coupled with a one-dimensional Ising system. The coupling gives rise to drastic changes both in the oscillator statics and dynamics. Firstly, there appears a second order phase transition, with the…
The dynamics of two active nonlinear resonators coupled to a linear resonator is studied theoretically. Possible stationary states and its dynamical stability are considered in detail. The spontaneous symmetry breaking is found and it is…
Synchronization in oscillatory systems is a frequent natural phenomenon and is becoming an important concept in modern physics. Nanomechanical resonators are ideal systems for studying synchronization due to their controllable oscillation…
Complex dynamics of a ring cavity filled by the medium with cubic phase non-linearity driven by an external multi-frequency signal is studied. To describe the dynamics of envelope amplitudes the system of coupled Ikeda maps was derived. 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 numerical procedure designed to tune the parameters of periodically-driven dynamical systems to a state in which they exhibit rich dynamical behavior. This is achieved by maximizing the diversity of subharmonic…
A novel point of view on the phenomenon of self-pulsations is presented, which shows that they are a balanced state formed by two counteracting processes: beating of modes and bistable switching. A structure based on two coupled nonlinear…
We present sufficient conditions under which a given linear nonautonomous system and its nonlinear perturbation are topologically conjugated. Our conditions are of a very general form and provided that the nonlinear perturbations are…
Dynamic stabilization by simultaneous primary and superharmonic resonances for high order nonlinearity cancellation is demonstrated with an electrostatically-actuated, piezoresistively-transduced nanomechanical resonator. We prove…
Because of their nonlinearity, vibrational modes of resonantly driven nanomechanical systems have coexisting stable states of forced vibrations in a certain range of the amplitude of the driving force. Depending on its phase, which encodes…
We investigate the stochastic resonance phenomenon in a physical system based on a tunnel diode. The experimental control parameters are set to allow the control of the frequency and amplitude of the deterministic modulating signal over an…
Nonlinear light-matter interactions and their applications are constrained by properties of available materials. The use of metamaterials opens the way to achieve precise control over electromagnetic properties at a microscopic level,…