About Stability of Nonlinear Stochastic Differential Equations with State-Dependent Delay

被引：2

作者：

Shaikhet, Leonid ^{[1
]}

机构：

[1] Ariel Univ, Dept Math, IL-40700 Ariel, Israel

来源：

SYMMETRY-BASEL | 2022年 / 14卷 / 11期

关键词：

state-dependent delay; zero and positive equilibria; stochastic perturbations; asymptotic mean square stability; stability in probability; Lyapunov functionals construction; linear matrix inequalities (LMIs); SYSTEMS; CONTROLLABILITY; EXISTENCE;

D O I：

10.3390/sym14112307

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

A nonlinear stage-structured population model with a state-dependent delay under stochastic perturbations is investigated. Delay-independent and delay-dependent conditions of stability in probability for two equilibria of the considered system are obtained via the general method of Lyapunov functionals construction and the method of linear matrix inequalities (LMIs). The model under consideration is not the aim of the work and was chosen only to demonstrate the proposed research method, which can be used for the study of other types of nonlinear systems with a state-dependent delay.

引用

页数：12

共 19 条

[1] Numerical solution of stochastic state-dependent delay differential equations: convergence and stability
Akhtari, Bahar
[J]. ADVANCES IN DIFFERENCE EQUATIONS, 2019, 2019 (01)
[2] Existence and controllability results for second-order impulsive stochastic evolution systems with state-dependent delay
Arthi, G.
Park, Ju H.
Jung, H. Y.
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2014, 248 : 328 - 341
[3] Stability of epidemic model with time delays influenced by stochastic perturbations
Beretta, E
Kolmanovskii, V
Shaikhet, L
[J]. MATHEMATICS AND COMPUTERS IN SIMULATION, 1998, 45 (3-4) : 269 - 277
[4] On the problem of linearization for state-dependent delay differential equations
Cooke, KL
Huang, WZ
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1996, 124 (05) : 1417 - 1426
[5] Simple LMIs for stability of stochastic systems with delay term given by Stieltjes integral or with stabilizing delay
Fridman, Emilia
Shaikhet, Leonid
[J]. SYSTEMS & CONTROL LETTERS, 2019, 124 : 83 - 91
[6] Stabilization by using artificial delays: An LMI approach
Fridman, Emilia
Shaikhet, Leonid
[J]. AUTOMATICA, 2017, 81 : 429 - 437
[7] GIKHMAN I., 1972, STOCHASTIC DIFFERENT
[8] Kazmerchuk Y., 2004, Functional Differential Equations, V11, P77
[9] Kolmanovskii V., 1999, INTRO THEORY APPL FU
[10] Kolmanovskii V. B., 1986, STABILITY FUNCTIONAL

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