In this work, we derived an Abel–Jacobi–Liouville identity for the case of two-dimensional linear systems ODEs (ordinary differential equations) with reflection. We also present a conjecture general and application to coupled harmonic oscillators.

This paper presents a framework for modeling the phase noise in complementary metal–oxide–semiconductor (CMOS) ring oscillators. The analysis considers both linear and nonlinear operations, and it includes both device noise and digital switching noise coupled through the power supply and substrate. In this paper, we show that fast rail-to-rail switching is required in order to achieve low phase...

This paper addresses the amplitude and phase dynamics of a large system of nonlinearly coupled, non-identical damped harmonic oscillators, which is based on recent research in coupled oscillation in optomechanics. Our goal is to investigate the existence and stability of collective behaviour which occurs due to a play-off between the distribution of individual oscillator frequency and the type ...

Background: This paper describes an analytical study of a bandpass filter that is based on the dynamic response of electrostatically-driven MEMS oscillators. Method of Approach: Unlike most mechanical and electrical filters that rely on direct linear resonance for filtering, the MEM filter presented in this work employs parametric resonance. Results: While the use of parametric resonance improv...

We continue the study of a model for heat conduction [6] consisting of a chain of non-linear oscillators coupled to two Hamiltonian heat reservoirs at different temperatures. We establish existence of a Liapunov function for the chain dynamics and use it to show exponentially fast convergence of the dynamics to a unique stationary state. Ingredients of the proof are the reduction of the infinit...

We study the response of an ensemble of synchronized phase oscillators to an external harmonic perturbation applied to one of the oscillators. Our main goal is to relate the propagation of the perturbation signal to the structure of the interaction network underlying the ensemble. The overall response of the system is resonant, exhibiting a maximum when the perturbation frequency coincides with...

In this work we study the possibility of detecting the so-called strong stochasticity threshold (i.e., the transition between weak and strong chaos as the energy density of the system is increased) in anharmonic oscillator chains by means of the 0-1 test for chaos. We compare the result of the aforementioned methodology with the scaling behavior of the largest Lyapunov exponent computed by mean...

Coupled oscillators play an important role in many scientific fields, for example, in mechanics, electronics, and biology; see [1, 4] and references therein. In this paper we analyze two coupled oscillators, one of which is driven by an external periodic force. Important example of such a system is a dynamic vibration absorber which consists of a small mass, m2, attached to the primary vibratin...

We consider the energy flow between a classical one-dimensional harmonic oscillator and a set of N two-dimensional chaotic oscillators, which represents the finite environment. Using linear response theory we obtain an analytical effective equation for the system harmonic oscillator, which includes a frequency dependent dissipation, a shift, and memory effects. The damping rate is expressed in ...

The generation and control of animal locomotion is believed to involve central pattern generators - networks of neurons which are capable of producing oscillatory behavior. In the present work, the quadrupedal locomotor central pattern generator is modelled as four distinct but symmetrically coupled non-linear oscillators. We show that the typical patterns for two such networks of oscillators i...