Experimental observations of typical kinds of synchronization transitions are reported in unidirectionally coupled time-delay electronic circuits with a threshold nonlinearity and two time delays, namely feedback delay τ(1) and coupling delay τ(2). We have observed transitions from anticipatory to lag via complete synchronization and their inverse counterparts with excitatory and inhibitory cou...

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...

A time-delayed tumor cell growth model with correlated noises is investigated. In the condition of small delay time, the stationary probability distribution is derived and the stationary mean value (〈x〉st ) and normalized variance λ2 of the tumor cell population and state transition rate (κ) between two steady states are numerically calculated. The results indicate that: (i) The delay time (τ )...

Where f denotes Doppler Frequency, τ denotes multipath propagation delay, S (f,τ) denotes the scattering function. In a Power Delay Profile plot, the signal power of each multipath is plotted against their respective propagation delays. A sample power delay profile plot, shown below, indicates how a transmitted pulse gets received at the receiver with different signal strength as it travels thr...

and Applied Analysis 3 where the kernel K t, s is an n × n Cauchy matrix defined in the square a, b × a, b being, for every fixed s ≤ t , a solution of the matrix Cauchy problem LK ·, s t : ∂K t, s ∂t −A t Sh0K ·, s t Θ, K s, s I, 1.8 where K t, s ≡ Θ if a ≤ t < s ≤ b, Θ is n × n null matrix and I is n × n identity matrix. A fundamental n × n matrix X t for the homogeneous φ ≡ θ equation 1.5 ha...

In classical differential geometry, the problem of the determination of the position vector of an arbitrary space curve according to the intrinsic equations κ = κ(s) and τ = τ (s) (where κ and τ are the curvature and torsion of the space curve ψ, respectively) is still open [7, 14]. However, in the case of a plane curve, helix and general helix, this problem is solved. In this paper, we solved ...

In this paper, the perturbed continuous-time large-scale system with time delays is represented by an equivalent Takagi-Sugeno type fuzzy model. First, two types of decentralized state feedback controllers are considered in this paper. Based on the Riccati-type inequality, the Razumikhin theorem, and the delay-dependent Lyapunov functional approach, some controller design approaches are propose...

in this paper we initiate the study of real group algebras and investigate some of its aspects.let l1 (g) be a group algebra of a locally compact group g,τ :g →g be a group homeomorphismsuch that τ 2 =τοτ = 1, the identity map, and lp (g,τ ) = { f ∈ lp (g) : fοτ = f } ( p ≥ 1) . in thispaper, among other results, we clarify the structure of lp (g,τ ) and characterize amenability ofl1 (g,τ ) and...

Regard the stochastic differential delay equation dx(t)=[(A+Ā(t))x(t)+(B+B̄(t− τ)) x(t−τ)]dt+g(t,x(t),x(t−τ))dw(t) as the result of the effects of uncertainty, stochastic perturbation and time lag to a linear ordinary differential equation ẋ(t)=(A+B)x(t). Assume the linear system is exponentially stable. In this paper we shall characterize how much the uncertainty, stochastic perturbation and ti...

In this paper, we discuss the oscillatory behavior of first order delay differential equations of the form: y′(t) + p(t)y(τ(t)) = 0, t ≥ T, where p and T are continuous functions defined on [T,∞), p(t) > 0, τ(t) < t for t ≥ T, τ(t) is nondecreasing and lim t→∞ τ(t) = ∞. We present best possible conditions for the oscillation of all solutions for this equation.