相关论文: Koopman Spectrum for Cascaded Systems
Koopman spectral analysis has attracted attention for understanding nonlinear dynamical systems by which we can analyze nonlinear dynamics with a linear regime by lifting observations using a nonlinear function. For analysis, we need to…
Recently a Hamiltonian formulation for the evolution of the universe dominated by multiple oscillatory scalar fields was developed by the present author and was applied to the investigation of the evolution of cosmological perturbations on…
In this work, we consider a system of two wave equations coupled by velocities in one-dimensional space, with one boundary fractional damping. First, we show that the system is strongly asymptotically stable if and only if the coupling…
Driven quantum nonlinear oscillators, while essential for quantum technologies, are generally prone to complex chaotic dynamics that fall beyond the reach of perturbative analysis. By focusing on subharmonic bifurcations of a harmonically…
This is a review paper outlining recent progress in the spectral analysis of first order systems. We work on a closed manifold and study an elliptic self-adjoint first order system of linear partial differential equations. The aim is to…
The spectral fluctuations of complex quantum systems, in appropriate limit, are known to be consistent with that obtained from random matrices. However, this relation between the spectral fluctuations of physical systems and random matrices…
Oscillator networks found in social and biological systems are characterized by the presence of wide ranges of coupling strengths and complex organization. Yet robustness and synchronization of oscillations are found to emerge on…
The motivation of our research is to establish a Laplace-domain theory that provides principles and methodology to analyze and synthesize systems with nonlinear dynamics. A semigroup of composition operators defined for nonlinear autonomous…
The study of dissipation and decoherence in generic open quantum systems recently led to the investigation of spectral and steady-state properties of random Lindbladian dynamics. A natural question is then how realistic and universal those…
This paper addresses the problem of nonlinear state estimation for dynamical systems whose governing equations are approximated through Koopman operator liftings. While Koopman-based predictors have demonstrated broad approximation…
We derive the asymptotic distributions of the spiked eigenvalues and eigenvectors under a generalized and unified asymptotic regime, which takes into account the spike magnitude of leading eigenvalues, sample size, and dimensionality. This…
We study the entanglement dynamics of a system consisting of a large number of coupled harmonic oscillators in various configurations and for different types of nearest neighbour interactions. For a one-dimensional chain we provide compact…
We report on the dynamical formation of exceptional degeneracies in basic correlation functions of non-integrable one- and two-dimensional systems quenched to the vicinity of a critical point. Remarkably, fine-tuned semi-metallic points in…
Strassen's asymptotic spectrum offers a framework for analyzing the complexity of tensors. It has found applications in diverse areas, from computer science to additive combinatorics and quantum information. A long-standing open problem,…
A mathematical model is formulated for the evolution of plane perturbations in a cosmological two-component statistical system of completely degenerate scalarly charged fermions with an asymmetric scalar Higgs interaction. A complete closed…
Nonlinear coupled systems are ubiquitous in science and engineering. The analysis and modeling of such systems is challenging due to their high dimensionality and complex interactions among subsystems. In recent years, operator-theoretic…
Many natural systems, including neural circuits involved in decision making, are modeled as high-dimensional dynamical systems with multiple stable states. While existing analytical tools primarily describe behavior near stable equilibria,…
We study the dynamics of perturbations around nonthermal fixed points associated to universal scaling phenomena in quantum many-body systems far from equilibrium. For an N-component scalar quantum field theory in 3+1 space-time dimensions,…
Coupled oscillator networks show a complex interrelations between topological characteristics of the network and the nonlinear stability of single nodes with respect to large but realistic perturbations. We extend previous results on these…
Delay embeddings of time series data have emerged as a promising coordinate basis for data-driven estimation of the Koopman operator, which seeks a linear representation for observed nonlinear dynamics. Recent work has demonstrated the…