Texts in Applied Mathematics

Differential Equations and Dynamical Systems

Authors: Perko, Lawrence

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About this Textbook

 

This textbook presents a systematic study of the qualitative and geometric theory of nonlinear differential equations and dynamical systems.

Although the main topic of the book is the local and global behavior of nonlinear systems and their bifurcations, a thorough treatment of linear systems is given at the beginning of the text. All the material necessary for a clear understanding of the qualitative behavior of dynamical systems is contained in this textbook, including an outline of the proof and examples illustrating the proof of the Hartman-Grobman theorem, the use of the Poincare map in the theory of limit cycles, the theory of rotated vector fields and its use in the study of limit cycles and homoclinic loops, and a description of the behavior and termination of one-parameter families of limit cycles.

In addition to minor corrections and updates throughout, this new edition contains materials on higher order Melnikov functions and the bifurcation of limit cycles for planar systems of differential equations, including new sections on Francoise's algorithm for higher order Melnikov functions and on the finite codimension bifurcations that occur in the class of bounded quadratic systems.

Table of contents (4 chapters)

Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-1-4684-0249-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
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Bibliographic Information

Bibliographic Information
Book Title
Differential Equations and Dynamical Systems
Authors
Series Title
Texts in Applied Mathematics
Series Volume
7
Copyright
1996
Publisher
Springer-Verlag New York
Copyright Holder
Springer-Verlag New York, Inc.
eBook ISBN
978-1-4684-0249-0
DOI
10.1007/978-1-4684-0249-0
Series ISSN
0939-2475
Edition Number
2
Number of Pages
XIV, 519
Topics