Related papers: An efficient method for approximating resonance cu…
Phase-amplitude coupling (PAC), a form of cross-frequency interaction, has been implicated in various cognitive functions and, by extension, in neural communication and information integration. Accurately detecting and characterising PAC is…
The phase reduction method for a limit cycle oscillator subjected to a strong amplitude-modulated high-frequency force is developed. An equation for the phase dynamics is derived by introducing a new, effective phase response curve. We show…
Phase reduction is a general tool widely used to describe forced and interacting self-sustained oscillators. Here we explore the phase coupling functions beyond the usual first-order approximation in the strength of the force. Taking the…
Equations governing the nonlinear dynamics of complex systems are usually unknown and indirect methods are used to reconstruct their manifolds. In turn, they depend on embedding parameters requiring other methods and long temporal sequences…
Predictive design and optimization methods for controlled quantum systems depend on the accuracy of the system model. Any distortion of the input fields in an experimental platform alters the model accuracy and eventually disturbs the…
The strength of optomechanical interactions in a cavity optomechanical system can be quantified by a vacuum coupling rate $\vcr$ analogous to cavity quantum electrodynamics. This single figure of merit removes the ambiguity in the…
We explore oscillatory behaviour in a family of periodically driven spin chains which are subject to a weak measurement followed by post-selection. We discover a transition to an oscillatory phase as the strength of the measurement is…
We develop a tracking model predictive control (MPC) scheme for nonlinear systems using the linearized dynamics at the current state as a prediction model. Under reasonable assumptions on the linearized dynamics, we prove that the proposed…
Nonlinear waves are a robust phenomenon observed in complex systems ranging from mechanics to ecology. Fronts are fundamental due to their robustness against perturbations and capacity to propagate one state over another. Controlling and…
We propose a quantum mechanical method of detecting weak vibrational disturbances inspired by the protocol of entanglement farming. We consider a setup where pairs of atoms in their ground state are successively sent through an optical…
We investigate energy transfer and localization in a linear time-invariant oscillator chain weakly coupled to a forced nonlinear actuator. Two types of perturbation are studied: (1) harmonic forcing with a constant frequency is applied to…
We propose a time-adaptive predictor/multi-corrector method to solve hyperbolic partial differential equations, based on the generalized-$\alpha$ scheme that provides user-control on the numerical dissipation and second-order accuracy in…
The entrainment between weakly-coupled nonlinear oscillators, as well as between complex signals such as those representing physiological activity, is frequently assessed in terms of whether a stable relationship is detectable between the…
The present investigation deals with the dynamics of a two-degrees-of-freedom system which consists of a main linear oscillator and a strongly nonlinear absorber with small mass. The nonlinear oscillator has a softening hysteretic…
A robust energy transfer mechanism is found in nonlinear wave systems, which favours transfers towards modes interacting via triads with nonzero frequency mismatch, applicable in meteorology, nonlinear optics and plasma wave turbulence. We…
We consider semilinear hyperbolic systems with a trilinear nonlinearity. Both the differential equation and the initial data contain the inverse of a small parameter $\varepsilon$, and typical solutions oscillate with frequency proportional…
Real applications in structural mechanics, where the dynamic behavior is linear, are rare. Usually, structures are made of components assembled together by means of joints whose behavior maybe highly nonlinear. Depending on the amount of…
The dynamics of a one-degree of freedom oscillator with arbitrary polynomial non-linearity subjected to an external periodic excitation is studied. The sequences (cascades) of harmonic and subharmonic stationary solutions to the equation of…
Simple feedback loops, inspired from extremum-seeking, are proposed to lock a probe-frequency to the transition frequency of a single quantum system following quantum Monte-Carlo trajectories. Two specific quantum systems are addressed, a…
We analytically investigate the nonlinear response of a damped doubly clamped nanomechanical beam under static longitudinal compression which is excited to transverse vibrations. Starting from a continuous elasticity model for the beam, we…