Using the continuation theorem of coincidence degree theory and analysis techniques, we establish criteria for the existence of periodic solutions to the following third-order neutral delay functional differential equation with deviating arguments ... x (t) + aẍ(t) + g(ẋ(t− τ(t))) + f(x(t− τ(t))) = p(t). Our results complement and extend known results and are illustrated with examples.

We use Krasnoselskii’s fixed point theorem to show that the nonlinear neutral differential equation with delay d dt [x(t)− ax(t− τ)] = r(t)x(t)− f(t, x(t− τ)) has a positive periodic solution. An example will be provided as an application to our theorems. AMS Subject Classifications: 34K20, 45J05, 45D05

We propose a systemof partial differential equations with a single constant delay τ > 0 describing the behavior of a one-dimensional thermoelastic solid occupying a bounded interval of R. For an initial-boundary value problem associated with this system, we prove a well-posedness result in a certain topology under appropriate regularity conditions on the data. Further, we show the solution of o...

Sufficient conditions are established ensuring oscillation of all solutions of the odd-order neutral delay differential equation (x(t)− px(t− τ )) + m ∑ i=1 pix(t− σi) = 0, where p ∈ (−∞,∞), σi, pi, τ ∈ (0,∞). The present result improves some recent results.

The slowly maturing, long-lived rodent Octodon degus (degu) provides a unique opportunity to examine the development of the circadian system during adolescence. These studies characterize entrained and free-running activity rhythms in gonadally intact and prepubertally gonadectomized male and female degus across the first year in order to clarify the impact of sex and gonadal hormones on the ci...

We reveal in this paper that the environmental noise will not only suppress a potential population explosion in the stochastic delay Lotka–Volterra model but will also make the solutions to be stochastically ultimately bounded. To reveal these interesting facts, we stochastically perturb the delay Lotka–Volterra model ẋ(t) = diag(x1(t), . . . , xn(t))[b + Ax(t − τ)] into the Itô form dx(t)= dia...

This paper is aimed at the presentation and simulation verification of a novel simple and fast delay dependent stability (DDS) testing algorithm for linear timeinvariant time delay systems (LTI TDS). The algorithm can be used for systems with multiple delays and/or those with many controller parameters. Value ranges of delays and tunable parameters decide about the (exponential) stability of LT...

In this paper, the nonlinear systems with time-varying delays and parametric uncertainties are represented by an equivalent Takagi-Sugeno type fuzzy model. Based on Convex combination property, Lyapunov criterion, and Razumikhin theorem, some sufficient conditions are derived under which the parallel-distributed fuzzy control can stabilize the whole uncertain fuzzy time-delay systems asymptotic...

For many control systems in real life, impulses and delays are intrinsic phenomena that do not modify their controllability. So we conjecture that under certain conditions the abrupt changes and delays as perturbations of a system do not destroy its controllability. There are many practical examples of impulsive control systems with delays, such as a chemical reactor system, a financial system ...

IIn this paper, using frequency domain approach, a single mode laser model with delay is investigated. By choosing the delay τ as a bifurcation parameter, we show that Hopf bifurcation can occur when τ passes a sequence of critical values. This means that a family of periodic solutions bifurcate from the equilibrium when the bifurcation parameter exceeds a critical value. Some numerical simulat...