This paper is a review of applications of delay differential equations to different areas of engineering science. Starting with a general overview of delay models, we present some recent results on the use of retarded, advanced and neutral delay differential equations. An emerging area for modeling with the help of delay equations is real-time dynamic substructuring, or hybrid testing. We intro...

In this paper we give a brief overview of the application of delay differential equations with piecewise constant arguments (EPCAs) for obtaining numerical approximation of delay differential equations, and we show that this method can be used for numerical approximation in a class of age-dependent population models. We also formulate an open problem for a qualitative behaviour of a class of li...

We give an overview of how the Riccati equation makes its appearance in the stability analysis of linear systems with delays. We avoid complexities as time-invariance, added perturbations, distributed delays etc, to get to the main issues. Most generalizations can be or have been carried out, but do not add substantially to our understanding. We also show the connection between quadratic stabil...

A modified method for satellite attitude control system in presence of novel actuators is proposed in this paper. The attitude control system is composed of three fluidic momentum controller (FMC) actuators that are used to control Euler angles and their dynamics is considered in satellite attitude equations as well. L1 adaptive control is utilized for satellite three-axial ...

for the E-valued unknown function u, where E is a Banach space, B is the generator of a (linear) C0-semigroup on E, ut is the history function defined by ut(s) = u(t + s) and Φ is the delay operator. We will employ the semigroup approach on L-phase space (in the spirit of [4] and [5]) to be able to apply numerical splitting schemes to this problem. We prove convergence of theses schemes, invest...

memory‟. This approach is suitable for many mechanical systems, based on Newton‟s law: the current state (position + velocity) determines its future dynamics. But in many biological systems reaction does not come as immediate response to stimulation. It often appears with certain time-lags, so such systems are capable to accumulate past memory. Mathematically we can include time-lag, e.g. T in ...

The unification and extension of continuous calculus, discrete calculus, q-calculus, and indeed arbitrary real-number calculus to time-scale calculus, where a time scale is simply any nonempty closed set of real numbers, were first accomplished by Hilger in [4]. Since then, time-scale calculus has made steady inroads in explaining the interconnections that exist among the various calculuses, an...

Asymptotic methods for singularly perturbed delay differential equations are in many ways more challenging to implement than for ordinary differential equations. In this paper, four examples of delayed systems which occur in practical models are considered: the delayed recruitment equation, relaxation oscillations in stem cell control, the delayed logistic equation, and density wave oscillation...

We present an oscillation criterion for first order delay dynamic equations on time scales, which contains well-known criteria for delay differential equations and delay difference equations as special cases. We illustrate our results by applying them to various kinds of time scales.

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 ...