Evidence map›Paper›PMID 24489480›Full record

ArticleElectronic journal of qualitative theory of differential equations2013

Razumikhin-Type Stability Criteria for Differential Equations with Delayed Impulses.

Qing Wang, Quanxin Zhu

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Article in Electronic journal of qualitative theory of differential equations, 2013. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 3 papers.

0numbers the graph read from it
0cells of the map it votes in
3citing papers in PubMed
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1 · What the graph read from it

What it found

Each row is one number read from the abstract, on the scale the paper reported it, with its interval. Left of the dashed line favours the treatment, right favours the comparator. Under each row is the sentence it came from. New to these charts? A ten-minute tutorial.

The abstract states no effect estimate the extractor could read, or names no intervention and outcome on the map, so this paper lights no cell and moves no belief. It is still indexed, cited and linked below.

2 · The registry

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3 · Its place in the literature

Who cites it

3 citing papers in PubMed.

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4 · The record

Corrections and comments

PubMed lists nothing against this paper. Absence here is not a guarantee, only a check that was made.

5 · Who and what money

Authors and funding

2 authors.

Qing WangDepartment of Computer Sciences, Mathematics, and Engineering Shepherd University, Shepherdstown, WV 25443, USA.
Quanxin ZhuSchool of Mathematical Sciences and Institute of Mathematics Nanjing Normal University, Nanjing 210023, Jiangsu, China ; Department of Mathematics Ningbo University, Ningbo 315211, Zhejiang, China.

Funding

WV INBRE: The Inhibitor of Growth Family Member 4 (ING4) inhibits L-Type Amino Acid Transporter 1 (LAT1) expression to suppress Breast CancerP20GM103434 · NIGMS · MARSHALL UNIVERSITY · PI GARY O RANKIN · 2012 to 2026
$61.1M
NIGMS NIH HHS P20 GM103434
6 · The paper itself

Abstract

This paper studies stability problems of general impulsive differential equations where time delays occur in both differential and difference equations. Based on the method of Lyapunov functions, Razumikhin technique and mathematical induction, several stability criteria are obtained for differential equations with delayed impulses. Our results show that some systems with delayed impulses may be exponentially stabilized by impulses even if the system matrices are unstable. Some less restrictive sufficient conditions are also given to keep the good stability property of systems subject to certain type of impulsive perturbations. Examples with numerical simulations are discussed to illustrate the theorems. Our results may be applied to complex problems where impulses depend on both current and past states.

Indexed as

Global exponential stabilityImpulsive stabilizationLyapunov - Razumikhin methodSystems with delayed impulses

Identifiers

PMID24489480
PMCPMC3907520

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