Linear oscillators are used for modeling a diverse array of natural systems, for instance acoustics, materials science, and chemical spectroscopy. In this paper I describe simple models of structural interactions in biological molecules, known as elastic network models, as a useful topic for undergraduate biology instruction in mathematical modeling. These models use coupled linear oscillators ...

Recently, necessary and sufficient conditions for output synchronization of linear systems via diffusive couplings have been reported. In this paper, we study the case when such conditions are not satisfied and exact synchronization is impossible. In particular, we study two kinds of heterogeneous linear networks: (i) non-identical harmonic oscillators and (ii) double-integrators. We show that ...

−− This paper addresses the problem of testing continuous-time nuclear-pulse shapers using Oscillation-Based Test (OBT). The proposal is to convert the whole systems into non-linear oscillators, avoiding the partition in low-order sections. The design of the oscillators is very simple because the nonlinear elements are mathematically modeled using the describing function approach, and the study...

We perform experiments with 72 electronic limit-cycle oscillators, globally coupled via a linear or nonlinear feedback loop. While in the linear case we observe a standard Kuramoto-like synchronization transition, in the nonlinear case, with increase of the coupling strength, we first observe a transition to full synchrony and then a desynchronization transition to a quasiperiodic state. Howeve...

In undergraduate classrooms, while teaching chaos and fractals, it is taught as if there no relation between these two. By using some non linear oscillators we demonstrate that a connection fractals. plotting the phase space diagrams of four nonlinear box counting method finding fractal dimension established chaotic nature oscillators. The awareness all systems are good fractals will add more i...

Bispectral analysis, a technique based on high-order statistics, is extended to encompass time dependence for the case of coupled nonlinear oscillators. It is applicable to univariate as well as to multivariate data obtained, respectively, from one or more of the oscillators. It is demonstrated for a generic model of interacting systems whose basic units are the Poincaré oscillators. Their freq...

We investigate the interaction of a particle with a finite-size bath represented by a set of independent linear oscillators with frequencies that fall within a finite bandwidth. We discover that when the oscillators have particular frequency distributions, the finite-size bath behaves much as an infinite-size bath exhibiting dissipation properties and thus allowing irreversible energy absorptio...

We prove that any spectral sequence obeying a certain growth law is the quantum spectrum of an equivalence class of classically integrable non-linear oscillators. This implies that exceptions to the BerryTabor rule for the distribution of quantum energy gaps of classically integrable systems, are far more numerous than previously believed. In particular we show that for each finite dimension k,...

in this study, he’s variational approach (va) is used to solve the non-naturalvibrations and oscillations. the method works very well for the whole range of initial amplitudesand does not demand small perturbation. it is also sufficiently accurate to both linear and nonlinearphysics and engineering problems. we consider some examples to illustrate the effectiveness andconvenience of the method....