Related papers: Response of parametrically-driven nonlinear couple…

Optimization of mutual synchronization between a pair of limit-cycle oscillators with weak symmetric coupling is considered in the framework of the phase reduction theory. By generalizing a previous study on the optimization of…

In this work, the difficulties inherent to perturbative calculations in the velocity gauge are addressed. In particular, it is shown how calculations of nonlinear optical responses in the independent particle approximation can be done to…

We formulate a reduction theory that describes the response of an oscillator network as a whole to external forcing applied nonuniformly to its constituent oscillators. The phase description of multiple oscillator networks coupled weakly is…

An efficient technique is introduced for model inference of complex nonlinear dynamical systems driven by noise. The technique does not require extensive global optimization, provides optimal compensation for noise-induced errors and is…

We study the classical dynamics of a system comprising a pair of Kerr-Duffing nonlinear oscillators, which are coupled through a nonlinear interaction and subjected to a parametric drive. Using the rotating wave approximation (RWA), we…

This paper concerns the reliability of a pair of coupled oscillators in response to fluctuating inputs. Reliability means that an input elicits essentially identical responses upon repeated presentations regardless of the network's initial…

We have fabricated and studied a system of two tunable and coupled nonlinear superconducting resonators. The nonlinearity is introduced by galvanically coupled dc-SQUIDs. We simulate the system response by means of a circuit model, which…

We investigate the propagation of temperature perturbations in an array of coupled nonlinear oscillators at finite temperature. We evaluate the response function at equilibrium and show how the memory effects affect the diffusion…

We develop a perturbation-based frequency-response framework for analyzing amplification mechanisms that are central to subcritical routes to transition in wall-bounded shear flows. By systematically expanding the input-output dynamics of…

The non-linear response of infinite periodic solids to homogenous electric fields and collective atomic displacements is discussed in the framework of density functional perturbation theory. The approach is based on the 2n + 1 theorem…

A new method of inferencing of coupled stochastic nonlinear oscillators is described. The technique does not require extensive global optimization, provides optimal compensation for noise-induced errors and is robust in a broad range of…

We use radial basis functions to model the input--output response of an electronic device. A new methodology for producing models that accuratly describe the response of the device over a wide range of operating points is introduced. A key…

Coupled nonlinear oscillators can exhibit a wide variety of patterns. We study the Brusselator as a prototypical autocatalytic reaction diffusion model. Working in the limit of strong nonlinearity provides a clear timescale separation that…

Spin-torque oscillators are strong candidates as nano-scale microwave generators and detectors. However, because of large amplitude-phase coupling (non-linearity), phase noise is enhanced over other linear auto-oscillators. One way to…

This paper considers the dynamic response of a single degree of freedom system with nonlinear stiffness and nonlinear damping that is subjected to both resonant direct excitation and resonant parametric excitation, with a general phase…

Nonlinearity in macroscopic mechanical system plays a crucial role in a wide variety of applications, including signal transduction and processing, synchronization, and building logical devices. However, it is difficult to generate…

Mechanical sources of nonlinear damping play a central role in modern physics, from solid-state physics to thermodynamics. The microscopic theory of mechanical dissipation [M. I . Dykman, M. A. Krivoglaz, Physica Status Solidi (b) 68, 111…

Existence of amplitude independent frequencies of oscillation is an unusual property for a nonlinear oscillator. We find that a class of N coupled nonlinear Li\'enard type oscillators exhibit this interesting property. We show that a…

We present experimental observations of an anomaly in the coupled response of auto-parametrically excited microelectromechanical beams. When one of the two coupled beams is driven at elevated amplitudes, the excitation of dominant and…

Non-linear parametric resonances occur frequently in nature. Here we summarize how they can be studied by means of perturbative methods. We show in particular how resonances can affect the motion of a test particle orbiting in the vicinity…