Bifurcation Theory of Impulsive Dynamical Systems
Authors: Church, Kevin E.M., Liu, Xinzhi
Free Preview- Introduces new framework for nonautonomous dynamical systems
- Develops theoretical foundations of impulsive functional differential equations, including linear and nonlinear systems, stability, and invariant manifold theory
- Spotlights recent advances in stability and bifurcation
- Contains detailed calculations to support application-driven approach
- Delivers material in self-contained, three-part structure
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- About this book
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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.
- Table of contents (20 chapters)
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Introduction
Pages 3-20
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General Linear Systems
Pages 21-33
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Linear Periodic Systems
Pages 35-53
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Nonlinear Systems and Stability
Pages 55-66
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Existence, Regularity and Invariance of Centre Manifolds
Pages 67-109
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Table of contents (20 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Bifurcation Theory of Impulsive Dynamical Systems
- Authors
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- Kevin E.M. Church
- Xinzhi Liu
- Series Title
- IFSR International Series in Systems Science and Systems Engineering
- Series Volume
- 34
- Copyright
- 2021
- Publisher
- Springer International Publishing
- Copyright Holder
- Springer Nature Switzerland AG
- eBook ISBN
- 978-3-030-64533-5
- DOI
- 10.1007/978-3-030-64533-5
- Hardcover ISBN
- 978-3-030-64532-8
- Series ISSN
- 1574-0463
- Edition Number
- 1
- Number of Pages
- XVII, 388
- Number of Illustrations
- 17 b/w illustrations, 12 illustrations in colour
- Topics
