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Stability of Linear Delay Differential Equations

Many problems of growing interest in science, engineering, biology, and medicine
are modeled with systems of differential equations involving delay terms. In general, the presence of the delay in a model increases its reliability in describing the
relevant real phenomena and predicting its behavior. Besides, the introduction of
history in the evolution law of a system also augments its complexity since,
opposite to Ordinary Differential Equations (ODEs), Delay Differential Equations
(DDEs) represent infinite dimensional dynamical systems. Thus their time integration and the study of their stability properties require much more effort, together
with efficient numerical methods.
Since the introduction of the delay terms in the differential equations may
drastically change the system dynamics, inducing dangerous instability and loss of
performance as well as improving stability, analyzing the asymptotic stability of
either an equilibrium or a periodic solution of nonlinear DDEs is a crucial
requirement. Several monographs have been written on this subject and the theory
is well developed. By the Principle of Linearized Stability, the stability questions
can be reduced to the analysis of linear(ized) DDEs. In the literature, a great number
of analytical, geometrical, and numerical techniques have been proposed to answer
such questions. Part of these techniques aim at analyzing the distribution in the
complex plane of the eigenvalues of certain infinite dimensional linear operators, in
particular the solution operators associated to the linear(ized) problem and their
infinitesimal generator.

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Publisher
London : Springer.,
Collation
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Language
English
ISBN/ISSN
978-1-4939-2107-2
Classification
NONE
Content Type
text
Media Type
computer
Carrier Type
online resource
Edition
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Cataloger
Jemadi
Source
https://link.springer.com/content/pdf/10.1007/978-1-4939-2107-2.pdf?pdf=button
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