| Description |
1 online resource (xvii, 388 pages) : illustrations (some color) |
| Series |
IFSR international series in systems science and systems engineering, 1574-0463 ; volume 34 |
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IFSR international series on systems science and engineering ; v. 34. 1574-0463
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| Contents |
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 |
| 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 |
Includes bibliographical references and index |
| Notes |
Online resource; title from PDF title page (SpringerLink, viewed April 16, 2021) |
| Subject |
Bifurcation theory.
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System analysis.
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Dynamics.
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Mathematical models.
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Systems Analysis
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Models, Theoretical
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systems analysis.
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mathematical models.
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Análisis de sistemas
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Modelos matemáticos
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Bifurcation theory
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Dynamics
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Mathematical models
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System analysis
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Teoria de la bifurcació.
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Anàlisi de sistemes.
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| Genre/Form |
Llibres electrònics.
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| Form |
Electronic book
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| Author |
Liu, Xinzhi, 1956- author.
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| ISBN |
9783030645335 |
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3030645339 |
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