相关论文: Global computation of phase-amplitude reduction fo…

This paper proposes a novel formulation of frequency response for nonlinear systems in the Koopman operator framework. This framework is a promising direction for the analysis and synthesis of systems with nonlinear dynamics based on…

We present a new framework for optimal and feedback control of PDEs using Koopman operator-based reduced order models (K-ROMs). The Koopman operator is a linear but infinite-dimensional operator which describes the dynamics of observables.…

The Koopman operator allows for handling nonlinear systems through a (globally) linear representation. In general, the operator is infinite-dimensional - necessitating finite approximations - for which there is no overarching framework.…

This paper proposes a method for uncertainty quantification of an autoencoder-based Koopman operator. The main challenge of using the Koopman operator is to design the basis functions for lifting the state. To this end, this paper builds an…

In this paper, we address the problem of solving infinite-dimensional harmonic algebraic Lyapunov and Riccati equations up to an arbitrary small error. This question is of major practical importance for analysis and stabilization of…

Phase reduction is a powerful technique that makes possible describe the dynamics of a weakly perturbed limit-cycle oscillator in terms of its phase. For ensembles of oscillators, a classical example of phase reduction is the derivation of…

We present a program that implements the OPP reduction method to extract the coefficients of the one-loop scalar integrals from a user defined (sub)-amplitude or Feynman Diagram, as well as the rational terms coming from the 4-dimensional…

Phenomenological scaling arguments suggest the existence of universal amplitudes in the finite-size scaling of certain correlation lengths in strongly anisotropic or dynamical phase transitions. For equilibrium systems, provided that…

Any deterministic autonomous dynamical system may be globally linearized by its' Koopman operator. This object is typically infinite-dimensional and can be approximated by the so-called Dynamic Mode Decomposition (DMD). In DMD, the central…

For continuous-time dynamical systems with reversible trajectories, the nowhere-vanishing eigenfunctions of the Koopman operator of the system form a multiplicative group. Here, we exploit this property to accelerate the systematic…

Koopman operator describes evolution of observables in the phase space, which could be used to extract characteristic dynamical features of a nonlinear system. Here, we show that it is possible to carry out interesting symbolic partitions…

We provide an overview of the Koopman operator analysis for a class of partial differential equations describing relaxation of the field variable to a stable stationary state. We introduce Koopman eigenfunctionals of the system and use the…

Spectral decomposition of the Koopman operator is attracting attention as a tool for the analysis of nonlinear dynamical systems. Dynamic mode decomposition is a popular numerical algorithm for Koopman spectral analysis; however, we often…

Recently, several studies have investigated synchronization in quantum-mechanical limit-cycle oscillators. However, the quantum nature of these systems remained partially hidden, since the dynamics of the oscillator's phase was overdamped…

In this article, we explore the possibility of a sub-harmonic $(1{:}2)$ entrainment and supercritical Hopf bifurcation in a van der Pol-Duffing oscillator that has been excited by two frequencies, comprising a slow parametric drive and a…

Coupled oscillator networks provide mathematical models for interacting periodic processes. If the coupling is weak, phase reduction -- the reduction of the dynamics onto an invariant torus -- captures the emergence of collective dynamical…

Gas turbine engines are complex and highly nonlinear dynamical systems. Deriving their physics-based models can be challenging because it requires performance characteristics that are not always available, often leading to many simplifying…

We show how to extract the coefficients of the 4-, 3-, 2- and 1-point one-loop scalar integrals from the full one-loop amplitude of arbitrary scattering processes. In a similar fashion, also the rational terms can be derived. Basically no…

Rhythmic activity is ubiquitous in biological systems from the cellular to organism level. Reconstructing the instantaneous phase is the first step in analyzing the essential mechanism leading to a synchronization state from the observed…

We explore the phase reduction in networks of coupled oscillators in the higher orders of the coupling parameter. For coupled Stuart-Landau oscillators, where the phase can be introduced explicitly, we develop an analytic perturbation…