共查询到20条相似文献,搜索用时 15 毫秒
1.
In this paper we give a sufficient condition for the exponential asymptotic behavior of solutions of a general class of linear fractional stochastic differential equations with time-varying delays. Our obtained results allow us to employ the theories developed for the deterministic systems and to illustrate this, some examples are provided. 相似文献
2.
We study the asymptotic behavior of solutions of the following forced delay differential equation: Some sufficient conditions that guarantee every solution of the equation to converge to zero are obtained. The results obtained are applied to some well-known delay differential ecological equations with forcing term. 相似文献
3.
In this work, the asymptotic behavior of all solutions of second-order nonlinear ordinary differential equations with impulses is investigated. By impulsive differential inequality and Riccati transformation, sufficient conditions of asymptotic behavior of all solutions of second-order nonlinear ordinary differential equations with impulses are obtained. An example is also inserted to illustrate the impulsive effect. 相似文献
4.
This paper considers the asymptotic stability analysis of both exact and numerical solutions of the following neutral delay differential equation with pantograph delay.where $B,C,D\in C^{d\times d},q\in (0,1)$,and $B$ is regular. After transforming the above equation to non-automatic neutral equation with constant delay, we determine sufficient conditions for the asymptotic stability of the zero solution. Furthermore, we focus on the asymptotic stability behavior of Runge-Kutta method with variable stepsize. It is proved that a L-stable Runge-Kutta method can preserve the above-mentioned stability properties. 相似文献
5.
6.
In this paper, a new approach is provided to study the asymptotic behavior of functions. A Tauberian theorem is improved and applied to describe the asymptotic behavior of abstract functional differential equations of the form
7.
Julio G. Dix Ioannis K. Purnaras 《Journal of Mathematical Analysis and Applications》2006,318(1):296-304
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. 相似文献
8.
The aim of this work is to apply the method of “dichotomic maps” to study stability of the null solutions of delayed functional differential equations. Preliminaries are presented followed by proofs of main theorems on simple and asymptotic stability. Some particular cases which have been studied by others authors with more restrictive hypotheses and more elaborated methods are showed as illustrative examples enhancing the advantages of the dichotomic maps approach. 相似文献
9.
Hong-jiong Tian Li-qiang Fan Yuan-ying Zhang Jia-xiang Xiang 《计算数学(英文版)》2006,24(2):181-192
This paper deals with the relationship between asymptotic behavior of the numericalsolution and that of the true solution itself for fixed step-sizes. The numerical solution isviewed as a dynamical system in which the step-size acts as a parameter. We present aunified approach to look for bifurcations from the steady solutions into spurious solutionsas step-size varies. 相似文献
10.
Jiaoxun KuangHongjiong Tian Kaiting Shan 《Applied mathematics and computation》2011,217(24):10087-10094
We are concerned with delay-independent asymptotic stability of linear system of neutral differential equations. We first establish a sufficient and necessary condition for the system to be delay-independently asymptotically stable, and then give some equivalent stability conditions. This paper improves many recent results on the asymptotic stability in the literature. One example is given to show that the sufficient and necessary condition is easy to verify. 相似文献
11.
Alexander V. Rezounenko 《Journal of Mathematical Analysis and Applications》2007,326(2):1031-1045
This work is an attempt to treat partial differential equations with discrete (concentrated) state-dependent delay. The main idea is to approximate the discrete delay term by a sequence of distributed delay terms (all with state-dependent delays). We study local existence and long-time asymptotic behavior of solutions and prove that the model with distributed delay has a global attractor while the one with discrete delay possesses the trajectory attractor. 相似文献
12.
脉冲强迫非线性时滞微分方程的渐近性 总被引:3,自引:0,他引:3
本文研究一类脉冲强迫非线性时滞微分方程的渐近性,所得结果不仅适用于线性方程和非线性方程,强迫方程和非强迫方程,脉冲方程和非脉冲方程,而且改进了最近文献[8]的主要结果. 相似文献
13.
Hideaki Matsunaga 《Proceedings of the American Mathematical Society》2008,136(12):4305-4312
For a linear delay differential system with two coefficients and one delay, we establish some necessary and sufficient conditions on the asymptotic stability of the zero solution, which are composed of delay-dependent and delay-independent stability criteria. On the former criterion, the range of the delay is explicitly given.
14.
Jan Čermák Petr Kundrát Miroslav Urbánek 《Journal of Difference Equations and Applications》2013,19(6):567-580
The paper discusses the notion of a delay dynamic equation on time scales and describes some asymptotic properties of its solutions. The application of the derived results to continuous and discrete time scales presents new qualitative results for delay differential and difference equations. In particular, our approach faciliates the joint investigation of stability properties of the exact equations and their numerical discretizations. 相似文献
15.
The purpose of this paper is to investigate the asymptotic behavior of solutions of the forced nonlinear delay differential
equations with impulses
Our results, which hold for linear and nonlinear equations, forced and unforced equations, impulsive and nonimpulsive equations,
improve and generalize the known results recently obtained in [8].
Received September 7, 1997, Revised May 26, 1998, Accepted July 15, 1998 相似文献
16.
Randolph Rach 《Applied mathematics and computation》2011,217(12):5910-5922
The Adomian decomposition method and the asymptotic decomposition method give the near-field approximate solution and far-field approximate solution, respectively, for linear and nonlinear differential equations. The Padé approximants give solution continuation of series solutions, but the continuation is usually effective only on some finite domain, and it can not always give the asymptotic behavior as the independent variables approach infinity. We investigate the global approximate solution by matching the near-field approximation derived from the Adomian decomposition method with the far-field approximation derived from the asymptotic decomposition method for linear and nonlinear differential equations. For several examples we find that there exists an overlap between the near-field approximation and the far-field approximation, so we can match them to obtain a global approximate solution. For other nonlinear examples where the series solution from the Adomian decomposition method has a finite convergent domain, we can match the Padé approximant of the near-field approximation with the far-field approximation to obtain a global approximate solution representing the true, entire solution over an infinite domain. 相似文献
17.
研究了一类具有状态时滞的微分方程系统解的渐近行为,获得了该系统每一个有界解当t→∞时都趋于常向量,所获得的结果改进和扩展了已有文献的相关结果. 相似文献
18.
N. O. Sedova 《Russian Mathematics (Iz VUZ)》2008,52(11):60-69
We study certain sufficient conditions for the local and global uniform asymptotic stability, as well as the stabilizability of the equilibrium in cascade systems of delay differential equations. As distinct from the known results, the assertions presented in this paper are also valid for the cases, when the right-hand sides of equations are nonlinear and depend on time or arbitrarily depend on the historical data of the system. We prove that the use of auxiliary constant-sign functionals and functions with constant-sign derivatives essentially simplifies the statement of sufficient conditions for the asymptotic stability of a cascade. We adduce an example which illustrates the use of the obtained results. It demonstrates that the proposed procedure makes the study of the asymptotic stability and the construction of a stabilizing control easier in comparison with the traditional methods. 相似文献
19.
研究苍蝇追逐动态行为,针对不同的追逐行为建立了微分方程模型,利用数值模拟的方法分析模型的渐近行为,并结合微分方程的定性理论,讨论了苍蝇个体大小对追逐动态行为的影响. 相似文献
20.
广义时滞微分方程的渐近稳定性和数值分析 总被引:3,自引:0,他引:3
考虑了广义时滞微分方程的初值问题,分析了用线性多步法求解一类广义滞后型微分系统数值解的稳定性,在一定的Lagrange插值条件下,给出并证明了求解广义滞后型微分系统的线性多步法数值稳定的充分必要条件。 相似文献