Related papers: Projected Euler method for stochastic delay differ…
In this paper, we study the application of switched systems stability criteria to derive delay-dependent conditions for systems affected by both a constant and a time-varying delay. The main novelty of our approach lies on the use of…
In this paper, we obtain results on exponential stability of second order delay differential equations, which are based on a version of the Floquet theory for delay differential equations of the second order we proposed. Our version allows…
This work presents the design of nonlinear stabilization techniques for the finite element discretization of Euler equations in both steady and transient form. Implicit time integration is used in the case of the transient form. A…
In this paper we investigate explicit numerical approximations for stochastic differential delay equations (SDDEs) under a local Lipschitz condition by employing the adaptive Euler-Maruyama (EM) method. Working in both finite and infinite…
We consider the task of generating discrete-time realisations of a nonlinear multivariate diffusion process satisfying an It\^o stochastic differential equation conditional on an observation taken at a fixed future time-point. Such…
As the main contribution, this document provides a consistent discretization of a class of fixed-time stable systems, namely predefined-time stable systems. In the unperturbed case, the proposed approach allows obtaining not only a…
We consider the long-time behavior of an explicit tamed Euler scheme applied to a class of stochastic differential equations driven by additive noise, under a one-sided Lipschitz continuity condition. The setting encompasses drift…
In this paper, we establish the asymptotic stability of the steady-state for a 1-D stochastic Euler-Poisson equations with Ohmic contact boundary conditions forced by the Wiener process. We utilize Banach's fixed point theorem and the a…
This paper considers the initial value problem of general nonlinear stochastic fractional integro-differential equations with weakly singular kernels. Our effort is devoted to establishing some fine estimates to include all the cases of…
In finite-dimensional dynamical systems, stochastic stability provides the selection of physical relevant measures from the myriad invariant measures of conservative systems. That this might also apply to infinite-dimensional systems is the…
We consider stochastic dynamical systems defined by differential equations with a uniform random time delay. The latter equations are shown to be equivalent to deterministic higher-order differential equations: for an $n$-th order equation…
In this work, we adapt the {\em micro-macro} methodology to stochastic differential equations for the purpose of numerically solving oscillatory evolution equations. The models we consider are addressed in a wide spectrum of regimes where…
This work is the first attempt to treat partial differential equations with discrete (concentrated) state-dependent delay. The main idea is to approximate the discrete delay term by a sequence of distributed delay terms (all with…
A continuous-time average consensus system is a linear dynamical system defined over a graph, where each node has its own state value that evolves according to a simultaneous linear differential equation. A node is allowed to interact with…
To construct positivity-preserving numerical methods, a vast majority of existing works employ transformation techniques such as the Lamperti transformation or logarithmic transformation. However, using these techniques often leads to the…
We consider the use of adaptive timestepping to allow a strong explicit Euler-Maruyama discretisation to reproduce dynamical properties of a class of nonlinear stochastic differential equations with a unique equilibrium solution and…
We consider a nonlinear non-autonomous system with time-varying delays $$ \dot{x_i}(t)=-a_i(t)x_{i}(h_i(t))+\sum_{j=1}^mF_{ij}(t,x_j(g_{ij}(t))) $$ which has a large number of applications in the theory of artificial neural networks. Via…
This study aims to construct a stable, high-order compact finite difference method for solving Sobolev-type equations with Dirichlet boundary conditions in one-space dimension. Approximation of higher-order mixed derivatives in some…
The problem considered in the paper is exponential stability of linear equations and global attractivity of nonlinear non-autonomous equations which include a non-delay term and one or more delayed terms. First, we demonstrate that…
In this paper we develop necessary conditions for optimality, in the form of the stochastic Pontryagin maximum principle, for controlled equation with delay in the state and with control dependent noise, in the general case of controls $u…