Eigenvalues and delay differential equations: periodic coefficients, impulses and rigorous numerics
KEM Church - Journal of Dynamics and Differential Equations, 2021 - Springer
We develop validated numerical methods for the computation of Floquet multipliers of
equilibria and periodic solutions of delay differential equations, as well as impulsive delay …
equilibria and periodic solutions of delay differential equations, as well as impulsive delay …
Stability in the Critical Case and Bifurcations in Impulsive Systems
OV Anashkin, OV Yusupova - Lobachevskii Journal of Mathematics, 2021 - Springer
A one-parameter periodic impulsive system of the second order is considered. The
conditions for the appearance of the generic Andronov–Hopf bifurcation are discussed. It is …
conditions for the appearance of the generic Andronov–Hopf bifurcation are discussed. It is …
Invariant manifold-guided impulsive stabilization of delay equations
KEM Church, X Liu - IEEE Transactions on Automatic Control, 2021 - ieeexplore.ieee.org
We propose an impulsive stabilization method for delay equations based on a reduction to
the center-unstable manifold. Our approach does not make use of the constructions of …
the center-unstable manifold. Our approach does not make use of the constructions of …
Uniqueness of solutions and linearized stability for impulsive differential equations with state-dependent delay
KEM Church - Journal of Differential Equations, 2022 - Elsevier
We prove that under fairly natural conditions on the state space and nonlinearities, it is
typical for an impulsive differential equation with state-dependent delay to exhibit non …
typical for an impulsive differential equation with state-dependent delay to exhibit non …
User manual and tutorial for ISIM1s: a tiny MATLAB package for single stage invariant manifold-guided impulsive stabilization of delay equations
KEM Church - arXiv preprint arXiv:1912.07766, 2019 - arxiv.org
ISIM1s consists of a few MATLAB functions and a script that can be used to derive stabilizing
impulsive controllers for delay differential equations. This document serves as both a …
impulsive controllers for delay differential equations. This document serves as both a …