We study the existence of periodic solutions of the second order nonlinear neutral differential equation with variable delay x′′ (t) + p (t)x′ (t) + q (t)h (x (t)) = c (t)x′ (t− τ (t)) + f (t, x (t− τ (t))) . We invert the given equation to obtain an integral, but equivalent, equation from which we define a fixed point mapping written as a sum of a large contraction and a compact map. We show t...

We derive semiclassical periodic orbit expansions for a correlation function of the Wigner time delay. We consider the Fourier transform of the two-point correlation function, the form factorK(τ, x, y,M), that depends on the number of open channelsM , a non-symmetry breaking parameter x, and a symmetry breaking parameter y. Several terms in the Taylor expansion about τ = 0, which depend on all ...

This paper deals with the oscillations of numerical solutions for the nonlinear delay differential equations in physiological control systems. The exponential θ-method is applied to p′ t β0ω p t−τ / ω p t−τ −γp t and it is shown that the exponential θ-method has the same order of convergence as that of the classical θ-method. Several conditions under which the numerical solutions oscillate are ...

In this paper, oscillatory and asymptotic property of solutions of a class of nonlinear neutral delay differential equations of the form (E) d dt (r(t) d dt (y(t) + p(t)y(t− τ))) + f1(t)G1(y(t− σ1))− f2(t)G2(y(t− σ2)) = g(t) and d dt (r(t) d dt (y(t) + p(t)y(t− τ))) + f1(t)G1(y(t− σ1))− f2(t)G2(y(t− σ2)) = 0 are studied under the assumptions ∞ ∫ 0 dt r(t) <∞ and ∞ ∫

A variety of methods have been developed in nonlinear science to stabilize unstable periodic orbits (UPOs) and control chaos [1], following the seminal work by Ott, Grebogi and Yorke [2], who employed a tiny control force to stabilize UPOs embedded in a chaotic attractor [3, 4]. A particularly simple and efficient scheme is time-delayed feedback as suggested by Pyragas [5], which uses the diffe...

In this paper, the aim is to solve the neutral delay differential equations in the following form using multiquadric approximation scheme, (1){ y′(t) = f(t, y(t), y(t− τ(t, y(t))), y′(t− σ(t, y(t)))), t1 ≤ t ≤ tf , y(t) = φ(t), t ≤ t1, where f : [t1, tf ] × R × R × R → R is a smooth function, τ(t, y(t)) and σ(t, y(t)) are continuous functions on [t1, tf ]×R such that t−τ(t, y(t)) < tf and t− σ(...

where τ , e ∈ C(R,R) are T-periodic, and f , g ∈ C(R × R,R) are T-periodic in the first argument, T >  is a constant. In recent years, there are many results on the existence of periodic solutions for various types of delay differential equation with deviating arguments, especially for the Liénard equation and Rayleigh equation (see [–]). Now as the prescribed mean curvature ( x ′(t) √ +x′...

Blow-up phenomena are analyzed for both the delay-differential equation (DDE) u(t) = B(t)u(t− τ), and the associated parabolic PDE (PDDE) ∂tu = ∆u+B (t)u(t− τ, x), where B : [0, τ ] → R is a positive L function which behaves like 1/ |t− t∗| , for some α ∈ (0, 1) and t∗ ∈ (0, τ). Here B′ represents its distributional derivative. For initial functions satisfying u(t∗ − τ) > 0, blow up takes place...

By means of the averaging technique and the generalized Riccati transformation technique, we establish some oscillation criteria for the second-order quasilinear neutral delay dynamic equations r t |xΔ t |γ−1xΔ t Δ q1 t |y δ1 t |α−1y δ1 t q2 t |y δ2 t |β−1y δ2 t 0, t ∈ t0,∞ T, where x t y t p t y τ t , and the time scale interval is t0,∞ T : t0,∞ ∩ T. Our results in this paper not only extend t...