Pseudo-almost periodic solutions of neutral integral and differential equations with applications

The existence and uniqueness of pseudo-almost periodic solutions to general neutral integral equations with deviations are obtained. For this, pseudo-almost periodic functions in two variables are considered. The results extend the corresponding ones to the convolution type integral equations. They are used to study pseudo-almost periodic solutions of general neutral differential equations and to the so-called scalar neutral logistic equation version.     

一类二阶的中立型微分方程反周期解的存在性和唯一性

本文通过度理论,研究了如下的中立型微分方程的反周期解(u(t)-ku(t-r))"=f(u'(t))+g(u(t-r(t)))+p(t),得到了关于反周期解存在性和唯一性的新结果.本文所探讨的方程和使用的方法和已有的文献都有所不同.     

Positive periodic solutions for a neutral impulsive delayed Lotka–Volterra competition system with the effect of toxic substance

Based on the coincidence degree theory and its related continuation theorem as well as some a priori estimates, we explore the existence of periodic solutions with strictly positive components of a neutral delayed Lotka–Volterra competitive system with impulse. Easily verifiable sufficient criteria are established for the existence of positive periodic solution for the neutral impulsive system. When the results reduce to neutral system without impulse, they generalize the results in Yang and Cao [Positive periodic solutions of neutral Lotka–Volterra system with periodic delays, Appl. Math. Comput. 149 (2004) 661–687].     

非线性二阶中立型微分方程的振动性

考虑中立型微分方程我们建立了方程(1)的若干振动准则。这些结果适用于强超线性和强次线性中立型微分方程,且当p(t)≡0时仍然成立。     

二阶半线性中立型差分方程的振动性准则

考虑二阶半线性中立型差分方程给出了方程(1)的解的振动性的充分条件．所有结果推广和改进了关于中立和时滞差分方程已有结果．     

具有混合时滞的中立型Hopfield神经网络的概周期解

研究一类具有混合时滞的中立型Hopfield神经网络概周期解.通过运用指数二分性及不动点定理,获得了其概周期解的存在性与全局指数稳定性的充分条件,所得结果是新的,并且推广和改进了已有文献的相关结果.     

考虑偏差值的中立型区间交叉效率研究

在不确定性环境下,当决策单元(DMU)的投入产出数据为区间数形式时,为解决决策单元之间既不是合作也不是竞争关系时的交叉评价问题,本文提出一种中立型区间交叉效率模型。从所有被评价者的角度出发解决评价权重的选取问题,以决策单元投入得分的平均偏差与产出得分的平均偏差之和最小化为目标,建立决策单元在最佳和最差两种生产状态下的中立型区间交叉效率模型。在本文提出的中立型模型视角下,DMU的投入得分平均偏差和产出得分平均偏差之和达到最小。算例结果表明该中立型区间交叉效率模型的有效性,解决了不确定性环境下的交叉评价问题,保证评价的客观公正,更加符合现实。     

Asymptotic properties of neutral stochastic differential delay equations

This paper discusses asymptotic properties, especially asymptotic stability of neutral stochastic differential delay equations. New techniques are developed to cope with the neutral delay case, and the results of this paper are more general than the author's earlier work within the delay equations     

A Study on Oscillatory and Asymptotic Nature of Impulsive Neutral Differential Equations of Order Three

In this paper, we consider a class of third-order neutral impulsive differential equations. An equivalent class of neutral differential equations is obtained by using a suitable substitution. Some new oscillation results are proved. Moreover, we discuss the asymptotic behavior of the solution. The results presented here are illustrated via examples.     

Non-fragile guaranteed cost control for uncertain neutral dynamic systems with time-varying delays in state and control input

This article considers non-fragile guaranteed cost control problem for a class of uncertain neutral system with time-varying delays in both state and control input. Delay-dependent criteria are proposed to guarantee the robust stabilization of systems. Linear matrix inequality (LMI) optimization approach is used to solve the non-fragile guaranteed cost control problem. Non-fragile guaranteed cost control for unperturbed neutral system is considered in the first step. Robust non-fragile guaranteed cost control for uncertain neutral system is designed directly from the unperturbed condition. An efficient approach is proposed to design the non-fragile guaranteed cost control for uncertain neutral systems. LMI toolbox of Matlab is used to implement the proposed results. Finally, a numerical example is illustrated to show the usefulness of the proposed results.     

非线性中立型泛函微分方程Runge-Kutta 法的稳定性和收敛性

本文涉及Runge-Kutta 法变步长求解非线性中立型泛函微分方程(NFDEs) 的稳定性和收敛性.为此, 基于Volterra 泛函微分方程Runge-Kutta 方法的B- 理论, 引入了中立型泛函微分方程Runge-Kutta 方法的EB (expanded B-theory)-稳定性和EB-收敛性概念. 之后获得了Runge-Kutta 方法变步长求解此类方程的EB - 稳定性和EB- 收敛性. 这些结果对中立型延迟微分方程和中立型延迟积分微分方程也是新的.     

Comparison theorems on the oscillation of even order nonlinear mixed neutral differential equations

This study purposes to present some new comparison theorems that guarantee the oscillation of all solutions of even order functional differential equations with a neutral term including both advanced and delayed arguments. The obtained results are based on comparisons with associated first-order delay differential inequalities and first-order delay differential equations, and they are applicable to the both cases where the neutral coefficients are unbounded and/or bounded. In the last section, several examples showing the applicability of the results are provided.     

具有分布偏差变元的二阶中立型方程的振动准则(英文)

利用Riccati变换及积分平均技巧,建立一类具有非线性中立项及分布偏差变元的二阶中立型方程的振动准则,我们的结果推广并改进了一些已有的结果.     

A further note on stability criteria for uncertain neutral systems with mixed delays

This paper is a further note on stability criteria for uncertain neutral systems with mixed delays. We firstly employed a new method to estimate the upper bound of the derivative of functional, and novel stability criteria are presented for nominal neutral system, which will obtain less conservatism. Then, several sufficient stability conditions are proposed for neutral systems with polytopic uncertainty and linear fractional norm-bound uncertainty. Lastly, three numerical examples are given to demonstrate the effectiveness and merit of the proposed results. In Appendix, the stability criteria in Lu et al. [21] are rectified.     

A NEW OSCILLATION CRITERION FOR FIRST ORDER NEUTRAL DELAY DIFFERENTIAL EQUATION

In this paper, a new sufficient condition for the oscillation of all solutions of first order neutral delay differential equations is obtained. Secondly, the result can also be extended to a general neutral differential equation, and many known results in the literatures are improved.     

Stability of linear multistep methods for nonlinear neutral delay differential equations in Banach space

This paper is devoted to investigating the nonlinear stability properties of linear multistep methods for the solution to neutral delay differential equations in Banach space. Two approaches to numerically treating the “neutral term” are considered, which allow us to prove several results on numerical stability of linear multistep methods. These results provide some criteria for choosing the step size such that the numerical method is stable. Some examples of application and a numerical experiment, which further confirms the main results, are given.     

Stability analysis of neutral type systems in Hilbert space

The asymtoptic stability properties of neutral type systems are studied mainly in the critical case when the exponential stability is not possible. We consider an operator model of the system in Hilbert space and use recent results on the existence of a Riesz basis of invariant finite-dimensional subspaces in order to verify its dissipativity. The main results concern the conditions of asymptotic non-exponential stability. We show that the property of asymptotic stability is not determinated only by the spectrum of the system but essentially depends on the geometric spectral characteristic of its main neutral term. Moreover, we present an example of two systems of neutral type which have both the same spectrum in the open left-half plane and the main neutral term but one of them is asymptotically stable while the other is unstable.     

On abstract degenerate neutral differential equations

We introduce a new abstract model of functional differential equations, which we call abstract degenerate neutral differential equations, and we study the existence of strict solutions. The class of problems and the technical approach introduced in this paper allow us to generalize and extend recent results on abstract neutral differential equations. Some examples on nonlinear partial neutral differential equations are presented.     

New stability analysis for linear neutral system via state matrix decomposition

This paper deals with the problem of delay-dependent stability for neutral systems. The matrix decomposition technique is employed to reduce the conservativeness of stability conditions. The main results are extended to the neutral system with time-varying uncertainties. The proposed methods are with simpler form in terms of LMI and better performance than the existing ones in the literatures. Numerical examples are given to illustrate the effectiveness of the proposed methods.