相关论文: A new class of generalized ordinary differential e…

Carleman linearization is a mathematical technique that transforms nonlinear dynamical systems into infinite-dimensional linear systems, enabling simplified analysis. Initially developed for ordinary differential equations (ODEs) and later…

Based on the concept of manifold valued generalized functions we initiate a study of nonlinear ordinary differential equations with singular (in particular: distributional) right hand sides in a global setting. After establishing several…

This paper establishes the stable invariant manifold for a new kind of differential equations defined by Kurzweil integral, so-called {\em generalized ODEs} on a Banach space. The nonlinear generalized ODEs are formulated as $$…

We propose a novel second-order ODE as the continuous-time limit of a Riemannian accelerated gradient-based method on a manifold with curvature bounded from below. This ODE can be seen as a generalization of the ODE derived for Euclidean…

This chapter presents a dynamical systems point of view of the study of systems with delays. The focus is on how advanced tools from bifurcation theory, as implemented for example in the package DDE-BIFTOOL, can be applied to the study of…

We consider the parabolic Lam\'{e} system on a bounded domain. We focus on two types of inequalities for higher-order derivatives of solutions. The first is related to an $L^p$-$L^p$ estimate locally in time in the Lebesgue space setting,…

We determine local topological types of binary differential equations of asymptotic curves at parabolic and flat umbilical points for generic $2$-parameter families of surfaces in $\mathbb P^3$ by comparing our projective classification of…

In the modelling of stochastic phenomena, such as quasi-reaction systems, parameter estimation of kinetic rates can be challenging, particularly when the time gap between consecutive measurements is large. Local linear approximation…

We unearth the interconnection between various analytical methods which are widely used in the current literature to identify integrable nonlinear dynamical systems described by third-order nonlinear ordinary differentiable equations…

We show that a recently introduced generalized scheme of quantum mechanics has connections to Li\'{e}nard and Levinson-Smith classes of nonlinear systems. For the Li\'{e}nard type, which has coefficients of odd and odd symmetry, we…

A local existence and uniqueness theorem for ODEs in the special algebra of generalized functions is established, as well as versions including parameters and dependence on initial values in the generalized sense. Finally, a Frobenius…

Continuous-time projected dynamical systems are an elementary class of discontinuous dynamical systems with trajectories that remain in a feasible domain by means of projecting outward-pointing vector fields. They are essential when…

In the analysis of parametrized nonautonomous evolutionary equations, bounded entire solutions are natural candidates for bifurcating objects. Appropriate explicit and sufficient conditions for such branchings, however, require to combine…

We prove the solvability in Sobolev spaces for both divergence and non-divergence form higher order parabolic and elliptic systems in the whole space, on a half space, and on a bounded domain. The leading coefficients are assumed to be…

The paper proposes an algorithm which could identify a general class of pdes describing dynamical systems with similar symmetries. The way that will be followed starts from a given group of symmetries, the determination of the invariants…

This study will explicitly demonstrate by example that an unrestricted infinite and forward recursive hierarchy of differential equations must be identified as an unclosed system of equations, despite the fact that to each unknown function…

This paper demonstrates the application of Bayesian Artificial Neural Networks to Ordinary Differential Equation (ODE) inverse problems. We consider the case of estimating an unknown chaotic dynamical system transition model from state…

The aim of this article is to highlight the interest to apply Differential Geometry and Mechanics concepts to chaotic dynamical systems study. Thus, the local metric properties of curvature and torsion will directly provide the analytical…

Two new approaches to solving first-order quasilinear elliptic systems of PDEs in many dimensions are proposed. The first method is based on an analysis of multimode solutions expressible in terms of Riemann invariants, based on links…

Discovering governing equations from data is critical for diverse scientific disciplines as they can provide insights into the underlying phenomenon of dynamic systems. This work presents a new representation for governing equations by…