共查询到20条相似文献,搜索用时 375 毫秒
1.
杨喜陶 《数学物理学报(A辑)》2008,28(5):870-878
作者通过Liapunov泛函建立了一类高维差分方程解一致稳定、一致渐近稳定及指数渐近稳定的充要条件. 此外, 作者还证明了解的一致渐近稳定性蕴含解的有界性, 同时也给出了概周期差分方程存在概周期解的一个充分条件. 相似文献
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Meng Fan Jiabu DishenQian Wan Ke Wang 《Journal of Mathematical Analysis and Applications》2002,276(2):545-560
Sufficient and necessary criteria are established for the uniform stability and uniformly asymptotic stability of solutions of neutral functional differential equations (NFDEs) with finite delay by using the Liapunov functional approach. We also prove that the uniformly asymptotic stability of solutions implies the existence of bounded solution. 相似文献
4.
《Applied Mathematics Letters》2003,16(5):695-701
In this paper, we study the stability of a class of impulsive functional differential equations with infinite delays. We establish a uniform stability theorem and a uniform asymptotic stability theorem, which shows that certain impulsive perturbations may make unstable systems uniformly stable, even uniformly asymptotically stable. 相似文献
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以相空间为基础,研究了具有无限时滞中立型泛函微分方程解的稳定性和有界性,建立了方程解为一致稳定,一致渐近稳定的充要性判据;证明了当方程右端泛函满足Lipschitz条件时,解的一致渐近稳定性蕴涵了有界解的存在性,推广了文献[4-6]中已有的相关结果. 相似文献
6.
It is shown that uniform asymptotic stability does not imply exponential stability in linear Volterra difference equations. However, if the kernel of the equation decays exponentially. then both concepts are equivalent as in the case of ordinary difference equations. 相似文献
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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
8.
Masakazu Onitsuka 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(3-4):1266-1274
Sufficient conditions are established for non-uniform asymptotic stability of a linear oscillator with damping term. The obtained results clarify a difference between the uniform asymptotic stability and the asymptotic stability. Some simple examples are included to illustrate the results. Especially, Bessel’s differential equations are taken up and it is proved that the equilibrium is asymptotically stable, but it is not uniformly asymptotically stable. 相似文献
9.
Asymptotic Behavior of Solutions of Dynamic Equations 总被引:1,自引:0,他引:1
We consider linear dynamic systems on time scales, which contain as special cases linear differential systems, difference systems, or other dynamic systems. We give an asymptotic representation for a fundamental solution matrix that reduces the study of systems in the sense of asymptotic behavior to the study of scalar dynamic equations. In order to understand the asymptotic behavior of solutions of scalar linear dynamic equations on time scales, we also investigate the behavior of solutions of the simplest types of such scalar equations, which are natural generalizations of the usual exponential function. 相似文献
10.
Asymptotical stability of almost periodic solution for an impulsive multispecies competition–predation system with time delays on time scales
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In this paper, we consider the almost periodic dynamics of an impulsive multispecies Lotka–Volterra competition system with time delays on time scales. By establishing some comparison theorems of dynamic equations with impulses and delays on time scales, a permanence result for the model is obtained. Furthermore, based on the permanence result, by studying the Lyapunov stability theory of impulsive dynamic equations on time scales, we establish the existence and uniformly asymptotic stability of a unique positive almost periodic solution of the system. Finally, we give an example to show the feasibility of our main results, and our example also shows that the continuous time system and its corresponding discrete time system have the same dynamics. Our results of this paper are completely new even if for both the case of the time scale and the case of the time scale . Copyright © 2017 John Wiley & Sons, Ltd. 相似文献
11.
The exponential asymptotic stability of singularly perturbed delay differential equations with a bounded lag 总被引:1,自引:0,他引:1
Hongjiong Tian 《Journal of Mathematical Analysis and Applications》2002,270(1):143-149
This paper is concerned with the exponential stability of singularly perturbed delay differential equations with a bounded (state-independent) lag. A generalized Halanay inequality is derived in Section 2, and in Section 3 a sufficient condition will be provided to ensure that any solution of the singularly perturbed delay differential equations (DDEs) with a bounded lag is exponentially stable uniformly for sufficiently small ε>0. This type of exponential asymptotic stability can obviously be applied to general delay differential equations with a bounded lag. 相似文献
12.
Bassem Ben Hamed Imen Ellouze Mohamed Ali Hammami 《Mediterranean Journal of Mathematics》2011,8(4):603-616
In this paper, we investigate the problem of global uniform practical exponential stability of a general nonlinear non autonomous
differential delay equations. Using the global uniform practical exponential stability of the corresponding differential equation
without delay, we show that the differential delay equation will remain globally uniformly practically exponentially stable
provided that the time-lag is small enough. Finally, some illustrative examples are given to demonstrate the validity of the
results. 相似文献
13.
Yong-Hui Xia Jibin Li Patricia J.Y. Wong 《Nonlinear Analysis: Real World Applications》2013,14(6):2231-2248
This paper considers the topological classification of non-autonomous dynamic equations on time scales. In this paper we show, by a counterexample, that the trivial solutions of two topologically conjugated systems may not have the same uniform stability. This is contrary to the expectation that two topologically conjugated systems should have the same topological structure and asymptotic behaviors. To counter this mismatch in expectation, we propose a new definition of strong topological conjugacy that guarantees the same topological structure, and in particular the same uniform stability, for the corresponding solutions of two strongly topologically conjugated systems. Based on the new definition, a new version of the generalized Hartman–Grobman theorem is developed. We also include some examples to illustrate the feasibility and effectiveness of the new generalized Hartman–Grobman theorem. 相似文献
14.
Manil T. Mohan 《Applicable analysis》2020,99(10):1795-1826
ABSTRACT In this work, we consider the two-dimensional stationary and non-stationary tidal dynamic equations and examine the asymptotic behavior of the stationary solution. We prove the existence and uniqueness of weak and strong solutions of the stationary tidal dynamic equations in bounded domains using compactness arguments. Using maximal monotonicity property of the linear and nonlinear operators, we also establish that the solvability results are even valid in unbounded domains. Later, we obtain a uniform Lyapunov stability of the steady state solution. Finally, we remark that the stationary solution is exponentially stable if we add a suitable dissipative term in the equation corresponding to the deviations of free surface with respect to the ocean bottom. This exponential stability helps us to ensure the mass conservation of the modified system, if we choose the initial data of the modified system as stationary solution. 相似文献
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We survey some of the fundamental results on the stability and asymptoticity of linear Volterra difference equations. The method of Z-transform is heavily utilized in equations of convolution type. An example is given to show that uniform asymptotic stability does not necessarily imply exponential stabilty. It is shown that the two notions are equivalent if the kernel decays exponentially. For equations of nonconvolution type, Liapunov functions are used to find explicit criteria for stability. Moreover, the resolvent matrix is defined to produce a variation of constants formula. The study of asymptotic equivalence for difference equations with infinite delay is carried out in Section 6. Finally, we state some problems. 相似文献
17.
Alexander O. Ignatyev 《PAMM》2007,7(1):2030031-2030032
A system of ordinary differential equations with impulse effect at fixed moments of time is considered. The system is assumed to have the zero solution. It is shown that the existence of a corresponding Lyapunov function is a necessary and sufficient condition for the uniform asymptotic stability of the zero solution. Restrictions on perturbations of the right-hand sides of differential equations and impulse effects are obtained under which the uniform asymptotic stability of the zero solution of the ‘unperturbed’ system implies the uniform asymptotic stability of the zero solution of the ‘perturbed’ system. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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Very recently, a new theory known as set dynamic equations on time scales has been built. In this paper, a phase space is built for set functional dynamic equations with infinite delay on time scales and sufficient criteria are established for the existence of periodic solutions of such equations, which generalize and incorporate as special cases some known results for set differential equations and for set difference equations when the time scale is the real number set or the integer set, respectively, moreover, for differential inclusions and difference inclusions if the variable under consideration is a single valued mapping. Our results show that one can unify the study of some continuous or discrete problems in the sense of (set) dynamic equations on general time scales. 相似文献
19.
A system of differential equations with impulse effect is considered. It is assumed that this system has an invariant set M. By means of the direct Lyapunov method, the necessary and sufficient conditions of its uniform asymptotic stability are obtained. The conditions on the perturbations of right hand sides of differential equations and impulse effects, under which the uniform asymptotic stability of the invariant set M of the “nonperturbed” system implies the uniform asymptotic stability of the invariant set of the “perturbed” system, are obtained. The stability properties of invariant sets of periodic systems are also studied. 相似文献
20.
Lumped parameter, compartmental models of the human intracranial system are studied through development of a hybrid asymptotic-numerical technique. Dimensionless variables are introduced so that disparate time scales can be identified, and analysis shows that the system of model equations varies over both a fast and a slow time scale. On the fast time scale, the 5 × 5 system of equations may be decoupled to give a reduced 3 × 3 system combined with two conservation laws for the cerebrospinal fluid and brain compartmental volumes, respectively. The stiffness condition of the reduced system is shown to be considerably improved over that of the original system. For the general nonlinear problem, a uniformly valid asymptotic approximation for large time is derived by a hybrid asymptotic-numerical technique. In the special case of the linear problem, where compliances and resistances are assumed to be constants, the uniform approximation for large time is obtained analytically. To verify accuracy, both asymptotic and hybrid asymptotic-numerical results are compared with direct numerical integration of the full system. Physiological interpretations of the results are also given. 相似文献