Results 21 to 30 of about 610,121 (312)
Almost sure exponential stability of numerical solutions for stochastic delay differential equations [PDF]
, 2010 Using techniques based on the continuous and discrete semimartingale convergence theorems, this paper investigates if numerical methods may reproduce the almost sure exponential stability of the exact solutions to stochastic delay differential equations (
A. Rodkina +28 more
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Electronic Journal of Qualitative Theory of Differential Equations, 2023 We add relevant references about which we learned after the completion of the initial work. We mainly show how the concept of exponential trichotomy can successfully replace the one of exponential dichotomy in some results from the paper in the title.
Adriana Buică
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Datko-type theorems concerning asymptotic behaviour of exponential type in mean [PDF]
Opuscula MathematicaIn this paper, we study the concept of exponential (in)stability in mean for stochastic skew-evolution semiflows, in which the exponential (in)stability in the classical sense is replaced by an average with respect to a probability measure.
Pham Viet Hai
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On the Stability of Some Exponential Polynomials
Journal of Mathematical Analysis and Applications, 1997 The authors deal with the transcendental equation of the type \[ (z+ pz+ q)\exp(\tau z)+ rz=0, \] where \(p\), \(q\), \(r\), \(\mathbb{R}\), \(\tau, p>0\), \(q>0\), \(r=0\), \(n=0,1,2\). The main results are concerned with the case \(n=0\), which is important in the stability theory of delay.
Plácido Z. Táboas +1 more
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Exponential stability of Hopfield neural networks of neutral type with multiple time-varying delays
AIMS Mathematics, 2021 This paper investigates the problem for exponential stability of Hopfield neural networks of neutral type with multiple time-varying delays. Different from the existing results, the states of the neurons involve multiple time-varying delays and time ...
Li Wan +3 more
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Almost sure and moment exponential stability in the numerical simulation of stochastic differential equations [PDF]
, 2007 Relatively little is known about the ability of numerical methods for stochastic differential equations (SDEs) to reproduce almost sure and small-moment stability.
Burrage K. +3 more
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Exponential stability and partial averaging
Journal of Mathematical Analysis and Applications, 2003 The initial value problem for the system \(\dot{x}(t)=\varepsilon f(\varepsilon t,t, x(t))\), \(x(t_{0})=x_{0}\), is considered, where \(\varepsilon >0\) is a small parameter. The corresponding partially averaged system is \(\dot{z}(t)=\varepsilon f^{0}(\varepsilon t,z(t))\), \(z(t_{0})=x_{0}\), with \(f^{0}(s,x)=\lim_{T\rightarrow \infty}\frac{1}{T ...
Grammel, G., Maizurna, Isna
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Abstract and Applied Analysis, 2012 The numerical approximation of exponential Euler method is constructed for semilinear stochastic differential equations (SDEs). The convergence and mean-square (MS) stability of exponential Euler method are investigated. It is proved that the exponential
Chunmei Shi, Yu Xiao, Chiping Zhang
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Asymptotic stability equals exponential stability, and ISS equals finite energy gain---if you twist your eyes [PDF]
, 1998 In this paper we show that uniformly global asymptotic stability for a family of ordinary differential equations is equivalent to uniformly global exponential stability under a suitable nonlinear change of variables.
Grüne, Lars +2 more
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Stability of constant retrial rate systems with NBU input* [PDF]
, 2016 We study the stability of a single-server retrial queueing system with constant retrial rate, general input and service processes. First, we present a review of some relevant recent results related to the stability criteria of similar systems. Sufficient
Avrachenkov, K. +3 more
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