Related papers: On a simple approach to nonlinear oscillators
Consider a periodically forced nonlinear system which can be presented as a collection of smaller subsystems with pairwise interactions between them. Each subsystem is assumed to be a massive point moving with friction on a compact surface,…
This manuscript contains technical details and proofs of recent results developed by the authors, pertaining to the design of nonlinear controllers from the experimental data measured on an existing feedback control system.
Many systems in physics, chemistry and biology exhibit oscillations with a pronounced random component. Such stochastic oscillations can emerge via different mechanisms, for example linear dynamics of a stable focus with fluctuations,…
The analysis of complex nonlinear systems is often carried out using simpler piecewise linear representations of them. A principled and practical technique is proposed to linearize and evaluate arbitrary continuous nonlinear functions using…
We study a family of nonholonomic mechanical systems. These systems consist of harmonic oscillators coupled through nonholonomic constraints. In particular, the family includes the so called contact oscillator, which has been used as a test…
Experimental investigation of the nonlinear dynamics of a quantum oscillator is a long standing goal of quantum physics. We propose a conditional method for inducing an arbitrary nonlinear potential on a quantum oscillator weakly…
In this paper, we study connections between the classical model-based approach to nonlinear system theory, where systems are represented by equations, and the nonlinear behavioral approach, where systems are defined as sets of trajectories.…
What prevents us from building super-high intensity accelerators? The answer is case-specific, but it often points to one of the following phenomena: machine resonances, various tune shifts (and spreads), and instabilities. These three…
We analyze how complicated a linear optical component has to be if it is to perform one of a range of functions. Specifically, we devise an approach to evaluating the number of real parameters that must be specified in the device design or…
In this paper, we derive a framework to understand the effect of imperfections on the phasematching spectrum of a wide class of nonlinear systems. We show that this framework is applicable to many physical systems, such as waveguides or…
We present a novel approach for learning nonlinear dynamic models, which leads to a new set of tools capable of solving problems that are otherwise difficult. We provide theory showing this new approach is consistent for models with long…
Synchronization of coupled harmonic oscillators is investigated. Coupling considered here is pairwise, unidirectional, and described by a nonlinear function (whose graph resides in the first and third quadrants) of some projection of the…
We point out that the phase reduction of stochastic limit cycle oscillators has been done incorrectly in the literature. We present a correct phase reduction method for oscillators driven by weak external white Gaussian noises. Numerical…
Numerical simulations show that a massive real scalar field in a nonlinear theory can form long-lived oscillating localized states. For a self-interacting scalar on a fixed background these objects are named oscillons, while for the…
We present here a simple analytical model for self-oscillations in nano-electro-mechanical systems. We show that a field emission self-oscillator can be described by a lumped electrical circuit and that this approach is generalizable to…
In this paper we consider a quasilinear singular anisotropic elliptic problem with a p-sublinear perturbation. We prove uniqueness of weak solutions and we provide necessary and sufficient conditions for the existence of weak solutions in…
Nonlinear filtering is a pivotal problem that has attracted significant attention from mathematicians, statisticians, engineers, and various other scientific disciplines. The solution to this problem is governed by the so-called filtering…
Non-linear effects in accelerator physics are important for both successful operation of accelerators and during the design stage. Since both of these aspects are closely related, they will be treated together in this overview. Some of the…
Nonlinear control-affine systems with time-varying vector fields are considered in the paper. We propose a unified control design scheme with oscillating inputs for solving the trajectory tracking and stabilization problems. This…
Filon-Clenshaw-Curtis rules are among rapid and accurate quadrature rules for computing highly oscillatory integrals. In the implementation of the Filon-Clenshaw-Curtis rules in the case when the oscillator function is not linear, its…