On the instability of linear nonautonomous delay systems

Raúl Naulin

Czechoslovak Mathematical Journal (2003)

  • Volume: 53, Issue: 3, page 497-514
  • ISSN: 0011-4642

Abstract

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The unstable properties of the linear nonautonomous delay system x ' ( t ) = A ( t ) x ( t ) + B ( t ) x ( t - r ( t ) ) , with nonconstant delay r ( t ) , are studied. It is assumed that the linear system y ' ( t ) = ( A ( t ) + B ( t ) ) y ( t ) is unstable, the instability being characterized by a nonstable manifold defined from a dichotomy to this linear system. The delay r ( t ) is assumed to be continuous and bounded. Two kinds of results are given, those concerning conditions that do not include the properties of the delay function r ( t ) and the results depending on the asymptotic properties of the delay function.

How to cite

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Naulin, Raúl. "On the instability of linear nonautonomous delay systems." Czechoslovak Mathematical Journal 53.3 (2003): 497-514. <http://eudml.org/doc/30794>.

@article{Naulin2003,
abstract = {The unstable properties of the linear nonautonomous delay system $x^\{\prime \}(t)=A(t)x(t)+B(t)x(t-r(t))$, with nonconstant delay $r(t)$, are studied. It is assumed that the linear system $y^\{\prime \}(t)=(A(t)+B(t))y(t)$ is unstable, the instability being characterized by a nonstable manifold defined from a dichotomy to this linear system. The delay $r(t)$ is assumed to be continuous and bounded. Two kinds of results are given, those concerning conditions that do not include the properties of the delay function $r(t)$ and the results depending on the asymptotic properties of the delay function.},
author = {Naulin, Raúl},
journal = {Czechoslovak Mathematical Journal},
keywords = {Liapounov instability; $h$-instability; instability of delay equations; nonconstant delays; Lyapounov instability; -instability; instability of delay equations; nonconstant delays},
language = {eng},
number = {3},
pages = {497-514},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the instability of linear nonautonomous delay systems},
url = {http://eudml.org/doc/30794},
volume = {53},
year = {2003},
}

TY - JOUR
AU - Naulin, Raúl
TI - On the instability of linear nonautonomous delay systems
JO - Czechoslovak Mathematical Journal
PY - 2003
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 53
IS - 3
SP - 497
EP - 514
AB - The unstable properties of the linear nonautonomous delay system $x^{\prime }(t)=A(t)x(t)+B(t)x(t-r(t))$, with nonconstant delay $r(t)$, are studied. It is assumed that the linear system $y^{\prime }(t)=(A(t)+B(t))y(t)$ is unstable, the instability being characterized by a nonstable manifold defined from a dichotomy to this linear system. The delay $r(t)$ is assumed to be continuous and bounded. Two kinds of results are given, those concerning conditions that do not include the properties of the delay function $r(t)$ and the results depending on the asymptotic properties of the delay function.
LA - eng
KW - Liapounov instability; $h$-instability; instability of delay equations; nonconstant delays; Lyapounov instability; -instability; instability of delay equations; nonconstant delays
UR - http://eudml.org/doc/30794
ER -

References

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