Related papers: Parameterization method for state-dependent delay …
Systems with time delay play an important role in modeling of many physical and biological processes. In this paper we describe generic properties of systems with time delay, which are related to the appearance and stability of periodic…
We prove the well-posedness results, i.e. existence, uniqueness, and stability, of the solutions to a class of nonlocal fully nonlinear parabolic partial differential equations (PDEs), where there is an external time parameter $t$ on top of…
The solvability of a delay differential equation arising in the construction of quadratic cost functionals, i.e. Lyapunov functionals, for a linear time-delay system with a constant and a distributed delay is investigated. We present a…
Compartmental ordinary differential equation (ODE) models are used extensively in mathematical biology. When transit between compartments occurs at a constant rate, the well-known linear chain trick can be used to show that the ODE model is…
Neural Ordinary Differential Equations (NODEs), a framework of continuous-depth neural networks, have been widely applied, showing exceptional efficacy in coping with some representative datasets. Recently, an augmented framework has been…
This paper develops methods for numerically solving stochastic delay-differential equations (SDDEs) with multiple fixed delays that do not align with a uniform time mesh. We focus on numerical schemes of strong convergence orders $1/2$ and…
The paper presents a general strategy to solve ordinary differential equations (ODE), where some coefficient depend on the spatial variable and on additional random variables. The approach is based on the application of a recently developed…
Differential equations (DEs) are commonly used to describe dynamic systems evolving in one (ordinary differential equations or ODEs) or in more than one dimensions (partial differential equations or PDEs). In real data applications the…
We propose a new discretization method for PDEs on moving domains in the setting of unfitted finite element methods, which is provably higher-order accurate in space and time. In the considered setting, the physical domain that evolves…
Given a state space, Assignment of Observables involves Taking Function spaces Thereover. At the classical level, the state space in question is phase space or configuration space. This assignment picks up nontrivialities when whichever…
In this paper, we are interested in path-dependent stochastic differential equations (SDEs) which are controlled by Brownian motion and its delays. Within this non-Markovian context, we give a H \"ormander-type criterion for the regularity…
Stochastic differential equations (SDEs) provide a flexible framework for modeling temporal dynamics in partially observed systems. A central task is to calibrate such models from data, which requires inferring latent trajectories and…
Delay-Differential Equations (DDEs) are the most common representation for systems with delay. However, the DDE representation is limited. In network models with delay, the delayed channels are low-dimensional and accounting for this…
This paper concerns the stability of analytical and numerical solutions of nonlinear stochastic delay differential equations (SDDEs). We derive sufficient conditions for the stability, contractivity and asymptotic contractivity in mean…
Ordinary and stochastic differential equations (ODEs and SDEs) are widely used to model continuous-time processes across various scientific fields. While ODEs offer interpretability and simplicity, SDEs incorporate randomness, providing…
Ordinary differential equations (ODE's) are widespread models in physics, chemistry and biology. In particular, this mathematical formalism is used for describing the evolution of complex systems and it might consist of high-dimensional…
In the present article, we discuss some aspects of the local stability analysis for a class of abstract functional differential equations. This is done under smoothness assumptions which are often satisfied in the presence of a…
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…
In this paper, the stability of fractional differential equations (FDEs) with unknown parameters is studied. FDEs bring many advantages to model the physical systems in the nature or man-made systems in the industry. Because this…
This paper develops an explicit spectral representation for solutions of a one-dimensional linear wave equation with a constant time delay. The model is considered on a bounded interval with non-homogeneous Dirichlet boundary data and a…