Stability of nontrivial solution of delay differential equations with state-dependent impulses

被引：17
|
作者：
Liu, XZ [1 ]
Wang, Q [1 ]
机构：
[1] Univ Waterloo, Dept Appl Math, Waterloo, ON N2L 3G1, Canada
来源：
APPLIED MATHEMATICS AND COMPUTATION | 2006年 / 174卷 / 01期
基金：
加拿大自然科学与工程研究理事会;
关键词：
stability; quasi-stability; impulsive differential equation; reduced system;
D O I：
10.1016/j.amc.2005.03.028
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper considers the stability problem of nontrivial Solutions of delay differential equations with state-dependent impulses. By using the concepts of reduced system and quasi-stability, the stability problem of a nontrivial solution of the impulsive delay differential equation with state-dependent impulses is converted to that of the trivial solution of the impulsive delay differential equation with fixed impulses. Several stability criteria are then established utilizing the known results for systems with fixed impulses. (c) 2005 Published by Elsevier Inc.
引用
收藏
页码：271 / 288
页数：18
相关论文
共 50 条
  • [21] Wellposedness of abstract differential equations with state-dependent delay
    Hernandez, Eduardo
    Azevedo, Katia A. G.
    Rolnik, Vanessa
    MATHEMATISCHE NACHRICHTEN, 2018, 291 (13) : 2045 - 2056
  • [22] Periodic Orbits of State-Dependent Delay Differential Equations
    Corbett, Noah
    Naudot, Vincent
    INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2025, 35 (01):
  • [23] Local bifurcations in differential equations with state-dependent delay
    Sieber, Jan
    CHAOS, 2017, 27 (11)
  • [24] On the problem of linearization for state-dependent delay differential equations
    Cooke, KL
    Huang, WZ
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1996, 124 (05) : 1417 - 1426
  • [25] TIME TRANSFORMATIONS FOR STATE-DEPENDENT DELAY DIFFERENTIAL EQUATIONS
    Brunner, H.
    Maset, S.
    COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2010, 9 (01) : 23 - 45
  • [26] On abstract neutral differential equations with state-dependent delay
    Eduardo Hernández
    Michelle Pierri
    Journal of Fixed Point Theory and Applications, 2018, 20
  • [27] Validated integration of differential equations with state-dependent delay
    Church, Kevin E. M.
    COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2022, 115
  • [28] State-dependent impulsive delay-differential equations
    Dubeau, F
    Karrakchou, J
    APPLIED MATHEMATICS LETTERS, 2002, 15 (03) : 333 - 338
  • [29] On abstract neutral differential equations with state-dependent delay
    Hernandez, Eduardo
    Pierri, Michelle
    JOURNAL OF FIXED POINT THEORY AND APPLICATIONS, 2018, 20 (03)
  • [30] On second order differential equations with state-dependent delay
    Hernandez, Eduardo
    Azevedo, Katia A. G.
    O'Regan, Donal
    APPLICABLE ANALYSIS, 2018, 97 (15) : 2610 - 2617
12345