This paper is concerned with the oscillation of certain third-order nonlinear delay differential equations with damping. We give new characterizations of oscillation of the third-order equation in terms of oscillation of a related, well-studied, second-order linear differential equation without damping. We also establish new oscillation results for the third-order equation by using the integral...

We describe a method to model nonlinear dynamical systems using periodic solutions of delay-differential equations. We show that any finitetime trajectory of a nonlinear dynamical system can be loaded approximately into the initial condition of a linear delay-differential system. It is further shown that the initial condition can be extended to a periodic solution of the delay-differential syst...

Linear scalar differential equations with distributed delays appear in the study of the local stability of nonlinear differential equations with feedback, which are common in biology and physics. Negative feedback loops tend to promote oscillation around steady states, and their stability depends on the particular shape of the delay distribution. Since in applications the mean delay is often th...

We describe a method to model nonlinear dynamical systems using periodic solutions of delay-differential equations. We show that any finitetime trajectory of a nonlinear dynamical system can be loaded approximately into the initial condition of a linear delay-differential system. It is further shown that the initial condition can be extended to a periodic solution of the delay-differential syst...

We discuss the existence of classes of quadratic time-frequency representations (QTFRs), e.g. Cohen, power, and generalized time-shift covariant, that satisfy a time-frequency (TF) concentration property. This important property yields perfect QTFR concentration along group delay curves. It also (1) simpli es the QTFR formulation and property kernel constraints as the kernel reduces from 2-D to...

In this paper, a numerical method named as Initial Value Technique (IVT) is suggested to solve singularly perturbed boundary value problems for second order ordinary differential equations of reactiondiffusion type with a delay (negative shift). In this technique, the original problem of solving the second order differential equation is reduced to solving four first order singularly perturbed d...

This paper is concerned with the almost sure exponential stability of the multidimensional nonlinear stochastic differential delay equation (SDDE) with variable delays of the form dx(t) = f(x(t−δ1(t)), t)dt+g(x(t−δ2(t)), t)dB(t), where δ1, δ2 : R+ → [0, τ ] stand for variable delays. We show that if the corresponding (nondelay) stochastic differential equation (SDE) dy(t) = f(y(t), t)dt + g(y(t...

In this paper we study the existence of mild solutions for abstract partial functional differential equation with state-dependent delay.

The problem of noise analysis in measuring the group delay introduced by a dispersive optical element by use of white-light interferometric cross correlation is investigated. Two noise types, detection noise and position noise, are specifically analyzed. Detection noise is shown to be highly sensitive to the spectral content of the white-light source at the frequency considered and to the tempo...

In this paper we are concerned with the asymptotic stability of the delay differential equation x′(t) = A0x(t) + n ∑