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In this set of lectures, we review briefly some of the recent developments in the study of the chaotic dynamics of nonlinear oscillators, particularly of damped and driven type. By taking a representative set of examples such as the…
Transport is called nonreciprocal when not only the sign, but also the absolute value of the current, depends on the polarity of the applied voltage. It requires simultaneously broken inversion and time-reversal symmetries, e.g., by the…
The Caldeira-Leggett Hamiltonian (Eq. (1) below) describes the interaction of a discrete harmonic oscillator with a continuous bath of harmonic oscillators. This system is a standard model of dissipation in macroscopic low temperature…
The recent demonstration of resonant tunneling transport in nitride semiconductors has led to an invigorated effort to harness this quantum transport regime for practical applications. In polar semiconductors, however, the interplay between…
In this paper an approach is outlined. With this approach some explicit algorithms can be applied to solve the initial value problem of $n-$dimensional damped oscillators. This approach is based upon following structure: for any…
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…
A method for solving model nonlinear equations describing plasma oscillations in the presence of viscosity and resistivity is given. By first going to the Lagrangian variables and then transforming the space variable conveniently, the…
New non-linear, spatially periodic, long wavelength electrostatic modes of an electron fluid oscillating against a motionless ion fluid (Langmuir waves) are given, with viscous and resistive effects included. The cold plasma approximation…
In this tutorial, three examples of stochastic systems are considered: A strongly-damped oscillator, a weakly-damped oscillator and an undamped oscillator (integrator) driven by noise. The evolution of these systems is characterized by the…
Harmonic oscillator chains connecting two harmonic reservoirs at different constant temperatures cannot act as thermal diodes, irrespective of structural asymmetry. However, here we prove that perfectly harmonic junctions can rectify heat…
We implement a capacitorless model of a VO2 oscillator by introducing into the circuit of a field-effect transistor and a VO2 thermal sensor, which provide negative current feedback with a time delay. We compare the dynamics of current and…
We report on a novel rectification phenomenon in a 2-D lattice network consisting of $N\times N$ sites with diode and AC source elements with controllable phases. A phase cascade configuration is described in which the current ripple in a…
In this paper, an adaptive nonlinear controller is designed for a parallel DC-DC converter system that feeds an unknown ZIP load, characterized by constant impedance (Z), constant current (I), and constant power (P), at the DC bus. The…
The observations of the dc voltage proportional to the persistent current on system of asymmetric superconductor loops at a non-zero resistance raise a question on a nature of this quantum phenomenon and its possibility in semiconductor and…
Asymptotic disturbance rejection (equivalently tracking) for nonlinear systems has been studied only in qualitative terms (the state is asymptotically stable under bounded disturbances). We show how to prove quantitative performance…
Using a matched filter technique, we derive the minimum variance, unbiased estimator for the equilibrium displacement of a damped harmonic oscillator in thermal equilibrium when interactions with the thermal bath are the leading source of…
We present a theoretical study of the optical response of a nonlinear oscillator formed by coupling a metal nanoparticle local surface plasmon resonance to excitonic degrees of freedom in a monolayer transition-metal dichalcogenide. We show…
We study the dynamics of a damped harmonic oscillator in the presence of a retarded potential with state-dependent time-delayed feedback. In the limit of small time-delays, we show that the oscillator is equivalent to a Li\'enard system.…
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…
We experimentally investigate the nonlinear response of a multilayer graphene resonator using a superconducting microwave cavity to detect its motion. The radiation pressure force is used to drive the mechanical resonator in an…