[HTML][HTML] Koopman–Hill stability computation of periodic orbits in polynomial dynamical systems using a real-valued quadratic harmonic balance formulation
In this paper, we generalize the Koopman–Hill projection method, which was recently
introduced for the numerical stability analysis of periodic solutions, to be included …
introduced for the numerical stability analysis of periodic solutions, to be included …
Exact and Optimal Quadratization of Nonlinear Finite-Dimensional Nonautonomous Dynamical Systems
Quadratization of polynomial and nonpolynomial systems of ordinary differential equations
(ODEs) is advantageous in a variety of disciplines, such as systems theory, fluid mechanics …
(ODEs) is advantageous in a variety of disciplines, such as systems theory, fluid mechanics …
Quadratized Taylor series methods for ODE numerical integration
Abstract We focus on Taylor Series Methods (TSM) and Automatic Differentiation (AD) for the
numerical solution of Ordinary Differential Equations (ODE) characterized by a vector field …
numerical solution of Ordinary Differential Equations (ODE) characterized by a vector field …
Data-driven system identification using quadratic embeddings of nonlinear dynamics
S Klus, JP N'Konzi - arxiv preprint arxiv:2501.08202, 2025 - arxiv.org
We propose a novel data-driven method called QENDy (Quadratic Embedding of Nonlinear
Dynamics) that not only allows us to learn quadratic representations of highly nonlinear …
Dynamics) that not only allows us to learn quadratic representations of highly nonlinear …
Dissipative quadratizations of polynomial ODE systems
Quadratization refers to a transformation of an arbitrary system of polynomial ordinary
differential equations to a system with at most quadratic right-hand side. Such a …
differential equations to a system with at most quadratic right-hand side. Such a …
[HTML][HTML] On the solution calculation of nonlinear ordinary differential equations via exact quadratization
F Carravetta - Journal of Differential Equations, 2020 - Elsevier
We show a general method allowing the solution calculation, in the form of a power series,
for a very large class of nonlinear Ordinary Differential Equations (ODEs), namely the real …
for a very large class of nonlinear Ordinary Differential Equations (ODEs), namely the real …
Inexact linear solves in model reduction of bilinear dynamical systems
The bilinear iterative rational Krylov algorithm (BIRKA) is a very popular, standard, and
mathematically sound algorithm for reducing bilinear dynamical systems that arise …
mathematically sound algorithm for reducing bilinear dynamical systems that arise …
A test for the generic strong accessibility of meromorphic nonlinear systems
This paper provides a new analytic test to check strong accessibility of nonlinear control
systems. This test can be applied to nonlinear systems described by meromorphic vector …
systems. This test can be applied to nonlinear systems described by meromorphic vector …
The double phospho/dephosphorylation cycle as a benchmark to validate an effective Taylor series method to integrate ordinary differential equations
The double phosphorylation/dephosphorylation cycle consists of a symmetric network of
biochemical reactions of paramount importance in many intracellular mechanisms. From a …
biochemical reactions of paramount importance in many intracellular mechanisms. From a …
Carleman Linearization of Partial Differential Equations
T Vaszary - arxiv preprint arxiv:2412.00014, 2024 - arxiv.org
Carleman linearization is a technique that embeds systems of ordinary differential equations
with polynomial nonlinearities into infinite dimensional linear systems in a procedural way …
with polynomial nonlinearities into infinite dimensional linear systems in a procedural way …