相关论文: Koopman Spectrum for Cascaded Systems

Koopman spectral theory has grown in the past decade as a powerful tool for dynamical systems analysis and control. In this paper, we show how recent data-driven techniques for estimating Koopman-Invariant subspaces with neural networks can…

We investigate instabilities in a stochastic mathematical model of cochlear dynamics. The cochlea is modeled as a spatio-temporal dynamical system made up of a spatially distributed array of coupled oscillators, together with the cochlear…

We prove that the decay of the eigenfunctions of harmonic oscillators, uniform electric or magnetic fields is not stable under 0-order complex perturbations, even if bounded, of these Hamiltonians, in the sense that we can produce solutions…

This paper presents a novel learning framework to construct Koopman eigenfunctions for unknown, nonlinear dynamics using data gathered from experiments. The learning framework can extract spectral information from the full nonlinear…

We present an approach to construct approximate Koopman-type decompositions for dynamical systems depending on static or time-varying parameters. Our method simultaneously constructs an invariant subspace and a parametric family of…

The Koopman framework is a popular approach to transform a finite dimensional nonlinear system into an infinite dimensional, but linear model through a lifting process, using so-called observable functions. While there is an extensive…

In the investigation of the evolution of cosmological perturbations in inflationary universe models the behavior of perturbations during the reheating stage is the most unclear point. In particular in the early reheating phase in which a…

This paper deals with stability of discrete-time switched linear systems whose all subsystems are unstable. We present sufficient conditions on the subsystems matrices such that a switched system is globally exponentially stable under a set…

In this paper we extend the Gaussian self-consistent method to permit study of the equilibrium and kinetics of conformational transitions for heteropolymers with any given primary sequence. The kinetic equations earlier derived by us are…

Koopman operator, as a fully linear representation of nonlinear dynamical systems, if well-defined on a reproducing kernel Hilbert space (RKHS), can be efficiently learned from data. For stability analysis and control-related problems, it…

A mathematical model of the evolution of plane perturbations in the cosmological statistical system of completely degenerated scalar-charged fermions with the Higgs scalar interaction is formulated. A complete closed system of differential…

The dynamics of a cascaded system that consists of two atom-cavity subsystems is studied by using the quantum trajectory method. Unwanted losses are included, such as photon absorption and scattering by the cavity mirrors and spontaneous…

We consider a singularly perturbed second order elliptic system in the whole space. The coefficients of the systems fast oscillate and depend both of slow and fast variables. We obtain the homogenized operator and in the uniform norm sense…

We consider general high-dimensional spiked sample covariance models and show that their leading sample spiked eigenvalues and their linear spectral statistics are asymptotically independent when the sample size and dimension are…

The steady states of dynamical processes can exhibit stable nontrivial phases, which can also serve as fault-tolerant classical or quantum memories. For Markovian quantum (classical) dynamics, these steady states are extremal eigenvectors…

We consider equivariant continuous families of discrete one-dimensional operators over arbitrary dynamical systems. We introduce the concept of a pseudo-ergodic element of a dynamical system. We then show that all operators associated to…

. We study the evolution of the distribution of eigenvalues of a $N\times N$ matrix subject to a random perturbation drawn from (i) a generalized Gaussian ensemble (ii) a non-Gaussian ensemble with a measure variable under the change of…

We propose a fully data-driven, Koopman-based framework for statistically robust control of discrete-time nonlinear systems with linear embeddings. Establishing a connection between the Koopman operator and contraction theory, it offers…

We find sufficient conditions for commutative non-autonomous systems on certain metric spaces to be topologically stable. In particular, we prove that (i) Every mean equicontinuous, mean expansive system with strong average shadowing…

In broadband quantum optical systems, nonlinear interactions among a large number of frequency components induce complex dynamics that may defy heuristic analysis. In this work we introduce a perturbative framework for factoring out…