Stability of impulsive stochastic differential equations in terms of two measures via perturbing Lyapunov functions

Zhang, Shuorui

doi:10.1016/j.amc.2011.10.082

Cited by 12 publications

(7 citation statements)

References 14 publications

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“…In the past decade, stochastic functional differential systems with impulsive effects (SFDSwIE), including stochastic delayed differential systems with impulsive effects (SDDSwIE), have received intensive attention and a great deal of stability results have been reported in the literature . However, nearly all these existing stability results are based on the infimum or supremum of impulsive intervals, that is,

\inf_{k \in double-struckN} {t_{k} - t_{k - 1}}

is bounded from below, or

\sup_{k \in double-struckN} {t_{k} - t_{k - 1}}

is bounded from above.…”

Section: Introductionmentioning

confidence: 99%

Exponential Stability Analysis for Stochastic Delayed Differential Systems with Impulsive Effects: Average Impulsive Interval Approach

Yao

Cao

Li³

et al. 2016

Asian Journal of Control

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This paper is concerned with the exponential stability analysis of stochastic delayed systems with impulsive effects. By using the average impulsive interval approach, and together with comparison lemma and Razumikhin techniques, sufficient conditions ensuring the moment exponential stability of the systems under consideration are established. A stability criterion for non‐delayed stochastic systems with impulses is also derived as a corollary. Compared with the existing stability results in the literature, which are usually based on the supremum or infimum of impulsive intervals, the results reported in this paper are less conservative. Two illustrative examples are provided to validate the effectiveness and advantages of our theoretical results.

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\inf_{k \in double-struckN} {t_{k} - t_{k - 1}}

is bounded from below, or

\sup_{k \in double-struckN} {t_{k} - t_{k - 1}}

is bounded from above.…”

Section: Introductionmentioning

confidence: 99%

Exponential Stability Analysis for Stochastic Delayed Differential Systems with Impulsive Effects: Average Impulsive Interval Approach

Yao

Cao

Li³

et al. 2016

Asian Journal of Control

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“…This complex dynamical behavior can be modeled by impulsive differential equations. Impulsive differential equations have become more important in recent years in some mathematical models of real processes and phenomena studied in physics, chemical technology, population dynamics, biotechnology, and economics; see [1][2][3][4][5][6][7][8]. There has been a significant development in impulse theory, in recent years, especially in the area of impulsive differential equations with fixed moments; see the monographs [9][10][11].…”

Section: Introductionmentioning

confidence: 99%

“…In [13], Fang and Li studied model (2) and gave an answer to the open problem 9.2 of [12]. But paper [13] required that ( ) ≥ 0, ( ) ≥ 0 and 0 ( ) > ( ), ( ) ≥ 0 or 0 ( ) ≤ ( ), ( ) ≤ 0 for ∈ [0, ], where 0 ( ) = ( )/(1 − ( )).…”

Section: Introductionmentioning

confidence: 99%

Positive Periodic Solution for the Generalized Neutral Differential Equation with Multiple Delays and Impulse

Luo

Zeng

2014

Journal of Applied Mathematics

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By using a fixed point theorem of strict-set-contraction, which is different from Gaines and Mawhin's continuation theorem and abstract continuation theory fork-set contraction, we established some new criteria for the existence of positive periodic solution of the following generalized neutral delay functional differential equation with impulse:x'(t)=x(t)[a(t)-f(t,x(t),x(t-τ1(t,x(t))),…,x(t-τn(t,x(t))),x'(t-γ1(t,x(t))),…,x'(t-γm(t,x(t))))], t≠tk, k∈Z+; x(tk+)=x(tk-)+θk(x(tk)), k∈Z+. As applications of our results, we also give some applications to several Lotka-Volterra models and new results are obtained.

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“…As well known, in the practice, many systems are subject to short-term disturbances, these disturbances are often described by impulses in the modeling process, therefore the impulsive systems arise in many scientific fields and there are many works were reported on impulsive systems [7][8][9][10][11][12][13][14][15][16]. In those works, the stability study for the impulsive system is one of the research focuses, see [11][12][13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

“…In those works, the stability study for the impulsive system is one of the research focuses, see [11][12][13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

Impulsive stabilization of delay difference equations and its application in Nicholson's blowflies model

Ding

2012

Adv Differ Equ

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In this article, we consider the impulsive stabilization of delay difference equations. By employing the Lyapunov function and Razumikhin technique, we establish the criteria of exponential stability for impulsive delay difference equations. As an application, by using the results we obtained, we deal with the exponential stability of discrete impulsive delay Nicholson's blowflies model. At last, an example is given to illustrate the efficiency of our results.

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Stability of impulsive stochastic differential equations in terms of two measures via perturbing Lyapunov functions

Cited by 12 publications

References 14 publications

Exponential Stability Analysis for Stochastic Delayed Differential Systems with Impulsive Effects: Average Impulsive Interval Approach

Exponential Stability Analysis for Stochastic Delayed Differential Systems with Impulsive Effects: Average Impulsive Interval Approach

Positive Periodic Solution for the Generalized Neutral Differential Equation with Multiple Delays and Impulse

Impulsive stabilization of delay difference equations and its application in Nicholson's blowflies model

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