IFSR International Series in Systems Science and Systems Engineering

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
see more benefits

Buy this book

eBook $109.00
price for USA in USD
  • ISBN 978-3-030-64533-5
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $139.99
price for USA in USD
  • ISBN 978-3-030-64532-8
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
About this book

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)

Table of contents (20 chapters)

Buy this book

eBook $109.00
price for USA in USD
  • ISBN 978-3-030-64533-5
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $139.99
price for USA in USD
  • ISBN 978-3-030-64532-8
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
Loading...

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
Book Title
Bifurcation Theory of Impulsive Dynamical Systems
Authors
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