Bifurcation theory of impulsive dynamical systems / Kevin E.M. Church, Xinzhi Liu.
Church, Kevin E. M., author.; Liu, Xinzhi, 1956- author.
2021
QA380
Available Online

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Title
Bifurcation theory of impulsive dynamical systems / Kevin E.M. Church, Xinzhi Liu.
Author
Church, Kevin E. M., author.
ISBN
9783030645335 (electronic bk.)
3030645339 (electronic bk.)
9783030645342 (print)
3030645347
9783030645359 (print)
3030645355
9783030645328
3030645320
DOI
https://doi.org/10.1007/978-3-030-64533-5
Published
Cham, Switzerland : Springer, [2021]
Language
English
Description
1 online resource (xvii, 388 pages) : illustrations (some color)
Item Number
10.1007/978-3-030-64533-5 doi
Call Number
QA380
Dewey Decimal Classification
515/.392
Summary
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.
Bibliography, etc. Note
Includes bibliographical references and index.
Access Note
Access limited to authorized users.
Digital File Characteristics
text file
PDF
Source of Description
Online resource; title from PDF title page (SpringerLink, viewed April 16, 2021).
Added Author
Liu, Xinzhi, 1956- author.
Series
IFSR international series on systems science and engineering ; v. 34. 1574-0463
Available in Other Form
Print version: 9783030645328
Linked Resources
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Record Appears in
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All Resources
Impulsive functional differential equations. Introduction
General linear systems
Linear periodic systems
Nonlinear systems and stability
Existence, regularity and invariance of centre manifolds
Computational aspects of centre manifolds
Hyperbolicity and the classical hierarchy of invariant manifolds
Smooth bifurcations
Finite-dimensional ordinary impulsive differential equations. Preliminaries
Linear systems
Stability for nonlinear systems
Invariant manifold theory
Bifurcations
Singluar and nonsmooth phenomena. Continuous approximation
Non-smooth bifurcations
Applications. Bifurcations in an impulsively damped or driven pendulum
The Hutchinson equation with pulse harvesting
Delayed SIR model with pulse vaccinaton and temporary immunity
Stage-structured predator-prey system with pulsed birth
Dynamics of an in-host viral infection model with drug treatment.

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