We discuss a quadratic criterion optimal control problem for stochastic linear system with delay in both state and control variables. This problem will lead to a kind of generalized forward-backward stochastic differential equations FBSDEs with Itô’s stochastic delay equations as forward equations and anticipated backward stochastic differential equations as backward equations. Especially, we p...

Introduction: The theory and application of linear and nonlinear delay differential equations is an important subject within physics and applied mathematics. There are several numerical approaches for solving linear and nonlinear delay differential equations. Aim: In this paper, differential transform method ( DTM ) is applied to numerical solution of linear and nonlinear delay differential equ...

Uncertain delay differential equation is a type of differential equations driven by a canonical Liu process. This paper mainly focuses on the stability of uncertain delay differential equations. At first, the concept of stability in measure, stability in mean and stability in moment for uncertain delay differential equations will be presented. In addition, the sufficient condition for uncertain...

The second-order delay differential equations often appear in the dynamical system, celestial mechanics, kinematics, and so forth. Some numerical methods for solving secondorder delay differential equations have been discussed, which include θ-method [1], trapezoidal method [2], and RungeKutta-Nyströmmethod [3].The variational iteration method (VIM) was first proposed by He [4, 5] and has been ...

So far there are not many results on the stability for stochastic functional differential equations with infinite delay. Themain aim of this paper is to establish some new criteria on the stability with general decay rate for stochastic functional differential equations with infinite delay. To illustrate the applications of our theories clearly, this paper also examines a scalar infinite delay ...

In this paper, the equivalence of the multiple time scales (MTS) method and the center manifold reduction (CMR) method is proved for computing the normal forms of ordinary differential equations and delay differential equations. The delay equations considered include general delay differential equations (DDE), neutral functional differential equations (NFDE) (or neutral delay differential equat...

An important question for human balance control concerns how the differential equations for the neural control of balance should be formulated. In this paper, we consider a discrete-time and a continuous-time delayed proportional-derivative-acceleration controller and establish the transition between them by means of the semi-discretization. We show that the critical delay, which limits stabili...