Invariant manifold-guided impulsive stabilization of delay equations

2021 ◽  
pp. 1-1
Author(s):  
Kevin Church ◽  
Xinzhi Liu
Keyword(s):  
Invariant Manifold ◽  
Delay Equations ◽  
Impulsive Stabilization

scholarly journals Twin semigroups and delay equations

2021 ◽  
Vol 286 ◽  
pp. 332-410
Author(s):  
O. Diekmann ◽  
S.M. Verduyn Lunel
Keyword(s):  
Delay Equations

scholarly journals Smooth Stable Manifold for Delay Differential Equations with Arbitrary Growth Rate

Axioms ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 105
Author(s):  
Lokesh Singh ◽  
Dhirendra Bahuguna
Keyword(s):  
Differential Equation ◽  
Growth Rate ◽  
Invariant Manifold ◽  
Delay Differential Equation ◽  
Delay Differential Equations ◽  
Stable Manifold ◽  
Exponential Dichotomy ◽  
Delay Differential ◽  
Stable Invariant ◽  
Nonuniform Exponential Dichotomy

In this article, we construct a C1 stable invariant manifold for the delay differential equation x′=Ax(t)+Lxt+f(t,xt) assuming the ρ-nonuniform exponential dichotomy for the corresponding solution operator. We also assume that the C1 perturbation, f(t,xt), and its derivative are sufficiently small and satisfy smoothness conditions. To obtain the invariant manifold, we follow the method developed by Lyapunov and Perron. We also show the dependence of invariant manifold on the perturbation f(t,xt).

scholarly journals Predator-Prey Interactions, Age Structures and Delay Equations

2014 ◽  
Vol 9 (1) ◽  
pp. 92-107 ◽  
Author(s):  
M. Mohr ◽  
M. V. Barbarossa ◽  
C. Kuttler
Keyword(s):  
Delay Equations ◽  
Predator Prey ◽  
Age Structures

scholarly journals Determinants and periodic solutions of delay equations

2005 ◽  
Vol 411 ◽  
pp. 356-363
Author(s):  
M.C. Crabb ◽  
A.J.B. Potter
Keyword(s):  
Periodic Solutions ◽  
Delay Equations

Impulsive stabilization of a class of singular systems with time-delays

Automatica ◽  
2017 ◽  
Vol 83 ◽  
pp. 28-36 ◽  
Author(s):  
Wu-Hua Chen ◽  
Wei Xing Zheng ◽  
Xiaomei Lu
Keyword(s):  
Time Delays ◽  
Singular Systems ◽  
Impulsive Stabilization
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