We present Lyapunov stability and asymptotic theorems for steady state solutions of general state-dependent delay differential equations (DDEs) using Lyapunov-Razumikhin methods. Our results apply to DDEs with multiple discrete delays, which may be nonautonomous the result, but autonomous (or periodically forced) result. main technique is replace DDE by a ordinary equation (ODE) where delayed t...

here, a predator-prey model with hassell-varley type functional responses is studied. some sufficient conditions are obtained for the permanence and global asymptotic stability of the system by using comparison theorem and constructing a suitable lyapunov functional. moreover, an example is illustrated to verify the results by simulation.

In this paper, we aim to study the neutral-type delayed Caputo fractional differential equations of form CDαxt−gt,xt=ft,xt,t∈t0,∞,t0≥0 with order 0<α<1, which can be used describe growth processes in real-life sciences at present depends on not only past state but also rate. Our ultimate goal is concentrate convergence solutions a predetermined constant by establishing linkage between equ...

Incremental stability is a property of dynamical and control systems, requiring the uniform asymptotic stability of every trajectory, rather than that of an equilibrium point or a particular time-varying trajectory. Similarly to stability, Lyapunov functions and contraction metrics play important roles in the study of incremental stability. In this paper, we provide characterizations and descri...

The classic GI=G=1 queueing model of which the tail of the service time and/or the interarrival time distribution behaves as t ?v S(t) for t ! 1, 1 < v < 2 and S(t) a slowly varying function at innnity, is investigated for the case that the traac load a approaches one. Heavy-traac limit theorems are derived for the case that these tails have a similar behaviour at innnity as well as for the cas...

By adopting on a notion of stochastic differential contraction, the paper presents new results on the incremental mean squared gain (IMSG) analysis of nonlinear systems with stochastic inputs. The relative power between two stochastic processes is defined as the asymptotic average (over time) of the second moment of the point-wise distance (in some metric) between the two processes. The IMSG of...

This paper presents a mathematical approach to properly account for uncertainty in wind resource assessment and wind energy production estimation. The evaluation of a wind resource and the subsequent estimation of the annual energy production (AEP) is a highly uncertain process. Uncertainty arises at all points in the process, from measuring the wind speed to the uncertainty in a power curve. A...

in this paper, we present a fractional mathematical model of a one-dimensional phase phase change problem (stefan problem) with latent heat a power function of position. this model includes space-time fractional derivatives in caputo sense and time dependent surface heat flux. an approximate solution of this model is obtained by optimal homotopy asymptotic method (oham) to find an approximate s...

in this paper we apply the homotopy perturbation method to derive the higher-order asymptotic distribution of the eigenvalues and eigenfunctions associated with the linear real second order equation of sturm-liouville type on $[0,pi]$ with neumann conditions $(y&apos;(0)=y&apos;(pi)=0)$ where $q$ is a real-valued sign-indefinite number of $c^{1}[0,pi]$ and $lambda$ is a real parameter.

the asymptotic behaviour of the sequence with general term $p_n=(varphi(1)+varphi(2)+cdots+varphi(n))/(1+2+cdots+n)$, is studied which appears in the studying of coprime integers, and an explicit bound for the difference $p_n-6/pi^2$ is found.