Téléchargez le livre : Bifurcation Theory of Impulsive Dynamical Systems

Bifurcation Theory of Impulsive Dynamical Systems

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Éditeur :

Springer


Collection :

IFSR International Series in Systems Science and Systems Engineering

Paru le : 2021-03-24

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Description

This monograph presents the most recent progress in bifurcation theory of impulsive dynamical systems with time delays and other functional dependence. It covers not only smooth local bifurcations, but also some non-smooth bifurcation phenomena that are unique to impulsive dynamical systems. The monograph is split into four distinct parts, independently addressing both finite and infinite-dimensional dynamical systems before discussing their applications. The primary contributions are a rigorous nonautonomous dynamical systems framework and analysis of nonlinear systems, stability, and invariant manifold theory. Special attention is paid to the centre manifold and associated reduction principle, as these are essential to the local bifurcation theory. Specifying to periodic systems, the Floquet theory is extended to impulsive functional differential equations, and this permits an exploration of the impulsive analogues of saddle-node, transcritical, pitchfork and Hopf bifurcations.
Readers will learn how techniques of classical bifurcation theory extend to impulsive functional differential equations and, as a special case, impulsive differential equations without delays. They will learn about stability for fixed points, periodic orbits and complete bounded trajectories, and how the linearization of the dynamical system allows for a suitable definition of hyperbolicity. They will see how to complete a centre manifold reduction and analyze a bifurcation at a nonhyperbolic steady state.
Pages
388 pages
Collection
IFSR International Series in Systems Science and Systems Engineering
Parution
2021-03-24
Marque
Springer
EAN papier
9783030645328
EAN PDF
9783030645335
Informations sur l'ebook
Nombre pages copiables
3
Nombre pages imprimables
38
Taille du fichier
7096 Ko
Prix
126,59 €
EAN EPUB
9783030645335
Informations sur l'ebook
Nombre pages copiables
3
Nombre pages imprimables
38
Taille du fichier
26532 Ko
Prix
126,59 €

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