skin aging is a continuous process that exhibits fine and deep wrinkles, thin and transparent skin, loss of underlying fat, dry skin and itch, following decreased collagen and elastin  synthesis. both extrinsic and intrinsic agents are considered in the pathogenesis on skin aging. extrinsic factors such as sun exposure, windy and dry weather, nutrition, and lifestyle may induce premature aging,...

This article is concerned with oscillatory behavior of a class of third order half-linear delay dynamic equation with damping ( r(x 2 ) ) (t)+ p(t) ( x 2 )γ (t)+ q(t)x (τ (t)) = 0, on an arbitrary time scaleTwith supT = ∞ and lim t→∞ τ(t) = ∞.We establish some new sufficient conditions which ensure that every solution oscillates or converges to zero. Example is given to illustrate our main resu...

In this article we study the existence of periodic solutions of the second order nonlinear neutral differential equation with functional delay d dt x (t) + p (t) d dt x (t) + q (t) x (t) = d dt g (t, x (t− τ (t))) + f ` t, x (t) , x (t− τ (t)) ́ . The main tool employed here is the Burton-Krasnoselskii’s hybrid fixed point theorem dealing with a sum of two mappings, one is a large contraction an...

We study some approximation schemes for a nonlinear filtering problem when the state process X is the solution of a stochastic delay diffusion equation, and the observation process is a noisy function of Xs for s ∈ [t− τ, t], where τ is a constant. The approximating state is given by means of an Euler discretization scheme, and the observation process is a noisy function of the approximating st...

In this paper, a FitzHugh-Nagumo model with time delays is investigated. The linear stability of the equilibrium and the existence of Hopf bifurcation with delay τ is investigated. By applying Nyquist criterion, the length of delay is estimated for which stability continues to hold. Numerical simulations for justifying the theoretical results are illustrated. Finally, main conclusions are given...

In the paper, we study a kind of time-delayed novel coronavirus pneumonia dynamical model with vaccination. This considers that people are vaccinated, and human immune system has series processes, which need certain time. We first obtain disease-free equilibrium basic reproduction number R0, unique endemic when R0 > 1. Then discuss stability different delays τ. For τ = 0, using Lyapunov functio...

A predator-prey system with disease in the predator is investigated, where the discrete delay τ is regarded as a parameter. Its dynamics are studied in terms of local analysis and Hopf bifurcation analysis. By analyzing the associated characteristic equation, it is found that Hopf bifurcation occurs when τ crosses some critical values. Using the normal form theory and center manifold argument, ...

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.

In this paper, some new oscillation criteria are obtained for the secondorder quasi-linear neutral delay differential equation ( r(t)| ( x(t) + p(t)x(τ(t)) )′|α−1(x(t) + p(t)x(τ(t)))′)′+ f ( t, x(σ(t)) ) = 0, t ≥ t0 under the case when ∫∞ t0 1 r 1 α (t) dt <∞. Our results improve and supplement some known results in the literature. An example is also provided to illustrate the main results.