For a certain class of neutral differential equations it is shown that these equations can serve as population models in the sense that they can be interpreted as special cases or caricatures of the standard Gurtin-MacCamy model for a population structured by age with birth and death rate depending on the total adult population. The delayed logistic equation does not belong to this class but th...

s of IWANASP, September 10 – 12, 2008, Ericeira, Portugal NUMERICAL METHODS FOR FRACTIONAL DIFFERENTIAL EQUATIONS WITH DELAY NICOLA E. BANKS Department of Mathematics, University of Chester Parkgate Road, Chester, CH1 4BJ, UK E-mail: [email protected] The aim of this talk is to present a prototype numerical algorithm for the solution of Fractional Differential Equations containing a Delay t...

This paper studies the link between the number of critical eigenvalues and the number of delays in certain classes of delay-differential equations. There are two main results. The first states that for k purely imaginary numbers which are linearly independent over the rationals, there exists a scalar delay-differential equation depending on k fixed delays whose spectrum contains those k purely ...

A human quiet standing stability is discussed in this paper. The model under consideration is proposed to be a delayed differential equation DDE withmultiplicative white noise perturbation. The method of the center manifold is generalized to reduce a delayed differential equation to a two-dimensional ordinary differential equation, to study delay-induced instability or Hopf bifurcation. Then, t...

A question which has been open in the theory of stochastic equations with delay for around 25 years is: what conditions on the coefficients of a linear stochastic functional differential equations characterise the mean square stability of the solution? In this talk, a simple proof is supplied for a one-dimensional linear Volterra equation. The arguments extend to equations with finite memory or...

In this paper, optimal control for stochastic linear singular Takagi–Sugeno (T–S) fuzzy delay system with quadratic performance is obtained using genetic programming (GP). To obtain the optimal control, the solution of matrix Riccati differential equation (MRDE) is computed by solving differential algebraic equation (DAE) using a novel and nontraditional GP approach. The GP solution is equivale...

We consider an Ito stochastic differential equation with delay, driven by brownian motion, whose solution, by an appropriate reformulation, defines a Markov process X with values in a space of continuous functions C, with generator L. We then consider a backward stochastic differential equation depending on X , with unknown processes (Y, Z), and we study properties of the resulting system, in p...

In this paper we investigate the asymptotic properties of all solutions of the delay differential equation y′(x) = a(x)y(τ (x)) + b(x)y(x), x ∈ I = [x0,∞). We set up conditions under which every solution of this equation can be represented in terms of a solution of the differential equation z′(x) = b(x)z(x), x ∈ I and a solution of the functional equation |a(x)|φ(τ (x)) = |b(x)|φ(x), x ∈ I.

We study first order linear delay differential equations with variable coefficients and constant delays. Using solutions to a characteristic equation, we show asymptotic properties of solutions to the delay equation. To illustrate the hypothesis of the main theorem, we present an example.