Related papers: Nonlinear phase-amplitude reduction of delay-induc…
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…
Discrete-time models are very convenient to simulate a nonlinear system on a computer. In order to build the discrete-time simulation models for the nonlinear feedback systems (which is a very important class of systems in many…
Delayed processes are ubiquitous in biological systems and are often characterized by delay differential equations (DDEs) and their extension to include stochastic effects. DDEs do not explicitly incorporate intermediate states associated…
We introduce an extension to the standard reduction of oscillatory systems to a single phase variable. The standard reduction is often insufficient, particularly when the oscillations have variable amplitude and the magnitude of each…
We derive a Cram\'er-Rao lower bound for the variance of Floquet multiplier estimates that have been constructed from stable limit cycles perturbed by noise. To do so, we consider perturbed periodic orbits in the plane. We use a periodic…
Network couplings of oscillatory large-scale systems, such as the brain, have a space-time structure composed of connection strengths and signal transmission delays. We provide a theoretical framework, which allows treating the spatial…
Many nonlinear systems are described by eigenmodes with amplitude-dependent frequencies, interacting strongly whenever the frequencies become commensurate at internal resonances. Fast energy exchange via the resonances holds the key to rich…
This paper presents a framework grounded in the theory of describing function (DF) and incremental-input DF to theoretically analyze the nonlinear oscillatory response of automated vehicles (AVs) car-following (CF) amidst traffic…
A general phase reduction method for a network of coupled dynamical elements exhibiting collective oscillations, which is applicable to arbitrary networks of heterogeneous dynamical elements, is developed. A set of coupled adjoint equations…
Phase-locked solutions of coupled oscillators are studied with asymmetric coupling strengths or inhomogeneous natural frequencies. The solutions show remarkable profiles of phase lags from the pacemaker corresponding to the ratio of upward…
We describe a flexible and modular delayed-feedback nonlinear oscillator that is capable of generating a wide range of dynamical behaviours, from periodic oscillations to high-dimensional chaos. The oscillator uses electrooptic modulation…
Periodically driven systems provide a novel route to control the topology of quantum materials. In particular, Floquet theory allows an effective band description of periodically-driven systems through the Floquet Hamiltonian. Here, we…
In this article, we propose a very efficient technique to enhance the dynamical robustness for a network of mean-field coupled oscillators experiencing aging transition. In particular, we present a control mechanism based on delayed…
The synchronization stability of a complex network system of coupled phase oscillators is discussed. In case the network is affected by disturbances, a stochastic linearized system of the coupled phase oscillators may be used to determine…
Motivated by recent experiments, we study the dynamics of a qubit quadratically coupled to its detector, a damped harmonic oscillator. We use a complex-environment approach, explicitly describing the dynamics of the qubit and the oscillator…
While periodically-driven phases offer a unique insight into non-equilibrium topology that is richer than its static counterpart, their experimental realization is often hindered by ubiquitous decoherence effects. Recently, we have proposed…
We report the first experimental observation of multiple transitions showing the emergence and disappearance of slowly decaying eigenmodes in a dissipative, Floquet electronic system with synthetic components. Conventional wisdom has it…
In the present work we examine the dynamics of a model for oscillons in 1-dimensional spacetime field theories with a cubic nonlinearity. We utilize a reduction of the model to first and third harmonics, which leads to a reduced partial…
We consider construction of effective Hamiltonians for periodically driven interacting systems in the case of resonant driving. The standard high-frequency expansion is not expected to converge due to the resonant creation of collective…
This paper introduces a stochastic framework for a recently proposed discrete-time delay estimation method in Laguerre-domain, i.e. with the delay block input and output signals being represented by the corresponding Laguerre series. A…