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§ 1 . Introduction Recently,Li啨nard typeequationhasbeenwidelyinvestigated ,manyexcellentresultshavebeenobtained .In [1],theauthorhasinvestigatedLi啨nard typeequation¨x +f1 (x) x +f2 (x) x2 +g(x) =0 ( 1)andadtainedmanyresultsonthequalitativebehaviorofequation ( 1) .FortheretardedLi啨nard typeequation¨x+f1 (x) x+f2 (x) x2 +φ(x) +g(x(t -h) ) =0 ,( 2 )wherehisanonnegativeconstant,f1 ,f2 ,φandgarecontinuousfunctionsonR ,theauthorsin [2 ]haveinvestigatedstabilityandbounde… 相似文献
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For Lipschitzian differential inclusions, we prove that the existence of suitable Lyapunov functions is necessary for uniform stability and uniform boundedness of solutions. 相似文献
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对具有分布时滞的非自治Cohen-Grossberg神经网络进行了研究.通过构造适当的Lyapunov函数,利用不等式分析方法,引入多参数,得到了一系列解的一致有界性且最终有界性和全局指数稳定性的判别准则. 相似文献
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本文研究了具有有限时滞中立型泛函微分方程解的有界性问题 ,得到了方程解的指数渐近稳定性蕴涵有界解的存在性的新的结果 相似文献
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给出时滞 Lienard方程 x″+f( x) x′+ax′( t-τ) +g( x( t-τ) ) =0 ,a 0 ,一致有界及全局渐近稳定的充分条件 .讨论一阶导数项 ax′( t-τ)对方程有界性及渐近稳定性的影响 . 相似文献
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Ulrich Krause 《Journal of Difference Equations and Applications》2013,19(4):343-356
Sufficient conditions are given under which the higher order difference equation x n+1= f(x n,x n-1,...,xn-k ), n=0,1,2,... generates an order preserving discrete dynamical system with respect to the discrete exponential ordering. It is shown that under the above monotonicity assumption the boundedness of all solutions as well as the local and global stability of an equilibrium hold if and only if they hold for the much simpler first order equation x n+1=h(x n ), where h(x)=f(x,x,…,x). As an application, a second order nonlinear difference equation from macroeconomics and a discrete analogue of a model of haematopoiesis are discussed. 相似文献
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The stochastic theta method gives a computational procedure for simulating ordinary stochastic differential equations. The method involves a free parameter, . Here, we characterise the precise value of beyond which the region of linear asymptotic stability of the method becomes unbounded. The cutoff point is seen to differ from that in the deterministic case. Computations that suggest further results are also given. 相似文献
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应用能量估计方法和Gagliardo-Nirenberg型不等式,讨论了带自扩散和交错扩散的三种群Lotka-Volterra竞争模型解的一致有界性和整体存在性,并由Lyapunov函数证明了该模型正平衡点的全局渐近稳定性. 相似文献
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Sufficient conditions for boundedness and continuity are obtained for stochastically continuous infinitely divisible processes, without Gaussian component, {Y(t),t T}, where T is a compact metric space or pseudo-metric space. Such processes have a version given by Y(t)=X(t)+b(t),tT where b is a deterministic drift function and
Here N is a Poisson random measure on a Borel space S with –finite mean measure , and
is a measurable deterministic function. Let : T2 R+ be a continuous pseudo–metric on T. Define the -Lipschitz norm of the sections of f by
for some t0 T, where D is the diameter of (T,). The sufficient conditions for boundedness and continuity of X are given in terms of the measure
and majorizing measure and or metric entropy conditions determined by . They are applied to stochastic integrals of the form
where M is a zero-mean, independently scattered, infinitely divisible random measure without Gaussian component. Several examples are given which show that in many cases the conditions obtained are quite sharp. In addition to obtaining conditions for continuity and boundedness, bounds are obtained for the weak and strong Lp norms of
and
for all
. These results depend on inequalities for moments and related functions of the weak and strong
norms of sequences {xj}, which are the events of Poisson point process M on R+ and are given in terms of the intensity measure of M. These results are of independent interest. 相似文献
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Cheng-jianZhang GengSun 《计算数学(英文版)》2004,22(3):447-456
In this paper, we deal with the boundedness and the asymptotic stability of linear and one-leg multistep methods for generalized pantograph equations of neutral type, which arise from some fields of engineering. Some criteria of the boundedness and the asymptotic stability for the methods are obtained. 相似文献
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BOUNDEDNESSANDBLOWUPFORTHEGENERALACTIVATOR-INHIBITORMODELLiMINGDE(李名德);CHENSHAOHUA(陈绍华);QINYUCHUN(秦禹春)(DepartmentofMathematic... 相似文献
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Connections between the spectral radius and the radius of boundedness are studied. Different characterizations of algebras (Q-property, strong saquentiality) are given in terms of these radii. Examples and applications are also provided. 相似文献
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In this paper, we consider the estimation of time-varying ARMA models subject to Markovian changes in regime. We give explicit conditions ensuring consistency and asymptotic normality, as well as the limiting covariance matrix, of least squares and quasi-generalized least-squares estimators. 相似文献
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In this paper, we introduce nonparametric ARMA models which provide an alternative to nonparametric autoregressive models,
when there is a large dependence to the past observations. Conditions for ergodicity and geometric ergodicity are given when
both the nonparametric autoregressive part and themoving average structure depend only one step behind. Also, a Fisher-consistent
procedure is provided and its performance is studied through a simulated example.
Received: 9 April 2002 相似文献
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The consistency proof for the (Gaussian quasi) maximum likelihood estimator in multivariable ARMA models as given in Dunsmuir and Hannan (1976, Adv, in Appl. Probab. 8, 339–364) rests on a certain property of the underlying parameter space, called B6 in their paper. It is not known whether the usual parameter spaces like the manifold M(n) or the parameter spaces corresponding to echelon forms satisfy condition B6, since the argument given by Dunsmuir and Hannan to establish this fact is inconclusive. In Pötscher (1987, J. Multivariate Anal. 21 29–52) it was shown how consistency can be proved without relying on B6 if the data generating process is Gaussian. In this note we show that the Gaussianity assumption can be replaced by ergodicity thus restoring Dunsmuir and Hannan's consistency proof to its full generality and extending it to parameter spaces which do not satisfy condition B6. 相似文献