Oscillation analysis of neutral difference equations with delays

In this paper, we obtain some oscillation criteria for a class of neutral difference equations with time delays. We also investigate the behavior of the eventually positive solutions of these equations. To verify our results we give various numerical simulations by using the MATLAB programming.     

Finite‐time stability of CNNs with neutral proportional delays and time‐varying leakage delays

In this paper, a class of cellular neural networks with neutral proportional delays and time‐varying leakage delays is considered. Some results on the finite‐time stability for the equations are obtained by using the differential inequality technique. In addition, an example with numerical simulations is given to illustrate our results, and the generalized exponential synchronization is also established. Copyright © 2016 John Wiley & Sons, Ltd.     

时标上的三阶非线性中立型变时滞动力方程的振动性与渐进性

考虑了时标上一类三阶非线性中立型变时滞动力方程的振动性和渐进性.利用Riccati变换技巧得到了方程所有解振动或渐进趋于零的充分条件.特别地,所得新结果发展了一些已有结论.并给出了例子加以说明本文的主要结果.     

Attracting and Invariant Sets of Nonlinear Stochastic Neutral Differential Equations with Delays

In this paper, a class of nonlinear stochastic neutral differential equations with delays is investigated. By using the properties of ${\mathcal{M}}$ -matrix, a differential-difference inequality is established. Basing on the differential-difference inequality, we develop a ${\mathcal{L}}$ -operator-difference inequality such that it is effective for stochastic neutral differential equations. By using the ${\mathcal{L}}$ -operator-difference inequality, we obtain the global attracting and invariant sets of nonlinear stochastic neutral differential equations with delays. In addition, we derive the sufficient condition ensuring the exponential p-stability of the zero solution of nonlinear stochastic neutral differential equations with delays. One example is presented to illustrate the effectiveness of our conclusion.     

Variable-step variable-order 3-stage Hermite-Birkhoff-Obrechkoff DDE solver of order 4 to 14

This article presents a solver for delay differential equations (DDEs) called HBO414DDE based on a hybrid variable-step variable-order 3-stage Hermite-Birkhoff-Obrechkoff ODE solver of order 4 to 14. The current version of our method solves DDEs with state dependent, non-vanishing, small, vanishing and asymptotically vanishing delays, except neutral type and initial value DDEs. Delayed values are computed using Hermite interpolation, small delays are dealt with by extrapolation, and discontinuities are located by a bisection method. HBO414DDE was tested on several problems and results were compared with those of known solvers like SYSDEL and the recent Matlab DDE solver ddesd and statistics show that it gives, most of the time, a smaller relative error than the other solvers for the same number of function evaluations.     

具有时滞的生态流行病模型的稳定性和Hopf分支

该文考虑一类食饵染病的时滞捕食被捕食模型. 作者分析了系统的非负不变性, 边界平衡点的性质和全局稳定性. 证明了当时滞τ=τ\-1+τ\-2适当小时, 正平衡点是局部渐近稳定的,随着时滞的增加, 正平衡点由稳定变为不稳定, 系统在正平衡点附近发生Hopf分支.     

非线性中立型抛物微分方程解的振动性

This paper deals with the oscillatory properties of a class of nonlinear neutral parabolic partial differential equations with several delays. Sufficient criteria for the equation to be oscillatory are obtained by making use of some results of first-order functional differential inequalities. These results fully reveal the essential difference between this type and that without delays.     

Stability of linear neutral differential equations with delays and impulses established by the fixed points method

In this paper, we consider the impulsive effects on the stability of the zero solution of the linear neutral differential equations with variable delays. By transforming the equations into ones without impulses and using fixed point theory, some sufficient conditions for asymptotic stability and exponential stability of the zero solution are obtained. The paper extends and improves results on sufficient conditions obtained by Jin and Luo (2008) [17], and Ardjouni and Djoudi (2011) [18], which is shown clearly in Example 1. This paper also shows that the impulse intensity and the impulse time both influence the decay rate of the convergence to zero of the solutions. Finally, two examples are given to show applications of some results obtained.     

Asymptotic properties of solutions to linear non-autonomous neutral differential equations

In this article we study asymptotic properties of solutions to first order linear neutral differential equations with variable coefficients and constant delays. Results are stated in terms of the solution to a characteristic equation. By doing this, we extend some of the results obtained for delay equations in [J.G. Dix, Ch.G. Philos, I.K. Purnaras, An asymptotic property of solutions to linear non-autonomous delay differential equations, Electron. J. Differential Equations 2005 (2005) 1-9] to neutral equations.     

变时滞高阶非线性中立型微分方程解的振动性、渐近性及分类

研究了变时滞高阶非线性中立型微分方程解的振动性和渐近性,并对方程解的分类进行了讨论,所得结论推广并改进了已知的一些结果.     

Positive periodic solutions for neutral functional differential equations with distributed delays and feedback control

By using a fixed point theorem of strict-set-contraction, some criteria are established for the existence of positive periodic solutions of neutral functional differential equations with distributed delays and feedback control.     

STUDY OF PERIODIC SOLUTIONS OF FOURTH ORDER NDE WITH DELAYS

Using Fourier series theory and techniques of real analysis inequality, some sufficient conditions of existence and uniqueness of periodic solutions for a class of fourth order neutral differential equations with some delays are obtained, the results extend and improve some known results.     

一类具有时变时滞的中立型系统的稳定性分析

本文研究一类具有状态时滞和输入时滞的时变时滞线性中立型系统.首先,通过选取合适的Lya-punov-Krasovskii泛函,应用LMI方法和Lyapunov-Krasovskii稳定性定理对时滞相关的系统进行稳定性分析,并设计了相应的控制器.改进了时不变时滞线性系统方面的一些结果.最后用实例验证所得到结果.     

Stability analysis of block boundary value methods for the neutral differential equation with many delays

This paper mainly deals with the asymptotic stability properties of block boundary value methods (B₂VMs) for the neutral differential equation with many delays. For the time lagging arguments, a technique of Lagrange interpolation is considered. Under some certain conditions, it is proved that B₂VMs can preserve the asymptotic stability of exact solutions for the neutral differential equation with many delays if and only if B₂VMs are A-stable for ordinary differential equation. Moreover, some numerical experiments are given to confirm the main conclusion.     

一类二阶半线性泛函微分方程的振动性

研究二阶半线性中立型分布时滞微分方程,利用Riccati变换,积分平均和不等式技巧,得到了一切解均为振动的若干新的振动准则,推广和改进了最近文献中的一些结果.     

Oscillation of Third-order Delay Dynamic Equations on Time Scales

This paper is concerned with the oscillatory behavior of a class of third-order noonlinear variable delay neutral functional dynamic equations on time scale. By using the generalized Riccati transformation and inequality technique, we establish some new oscilla- tion criteria for the equations. Our results extend and improve some known results, but also unify the oscillation of third-order nonlinear variable delay functional differential equations and functional difference equations with a nonlinear neutral term. Some examples are given to illustrate the importance of our results.     

Asymptotical stability analysis of Riemann‐Liouville q‐fractional neutral systems with mixed delays

This paper investigates the asymptotical stability of Riemann‐Liouville q‐fractional neutral systems with mixed delays (constant time delay and distributed delay). By constructing some appropriate Lyapunov‐Kravsovskii functionals, some sufficient conditions on delay‐dependent and delay‐independent asymptotical stability are obtained in terms of linear matrix inequality (LMI). Our employed method is based on the direct calculation of quantum derivatives of the Lyapunov‐Kravsovskii functionals. Finally, two examples are presented to demonstrate the availability of our obtained results.     

The RKHSM for solving neutral functional–differential equations with proportional delays

In this paper, the reproducing kernel Hilbert space method (RKHSM) is applied to neutral functional–differential equations with proportional delays. Its approximate solution is obtained by truncating the n‐term of exact solution. Some examples are displayed to demonstrate the computation efficiency of the method. We also compare the performance of the method with a particular Runge–Kutta method, a one‐leg θ‐method and variational iteration method. Experiment dates indicate that the RKHSM is an accurate and efficient method to solve neutral functional–differential equations with proportional delays. Copyright © 2012 John Wiley & Sons, Ltd.     

Global exponential convergence for a class of neutral functional differential equations with proportional delays

This paper is concerned with a class of non‐autonomous neutral functional differential equations with multi‐proportional delays. It is shown that all solutions of the addressed system are globally exponentially convergent by employing the differential inequality technique and a novel argument. The obtained results improve and supplement existing ones. We also use numerical simulations to demonstrate our theoretical results. Copyright © 2016 John Wiley & Sons, Ltd.     

$n$-维中立型多时滞微分方程的稳定性分析

This paper is mainly concerned with stability analysis of neutral differential equations with multiple delays. Some criteria on instability, stability, asymptotic stability and exponential stability are obtained. The criterion on asymptotic stability is necessary and sufficient. Two examples are provided to illustrate the applications of our results. Some previous results are extended.