By providing an introduction to nonlinear differential equations, author aims to equip the student with the mathematical know-how needed to appreciate stability theory and bifurcations.

This book covers material both old and new to undergraduate courses. Included are treatments of the Poincaré-Bendixson theorem, the Hopf bifurcation and chaotic systems.

Contents
Preface
Notation
1 Introduction
2 Stability
3 Linear differential equations
4 Linearization and hyperbolicity
5 Two-dimensional dynamics
6 Periodic orbits
7 Perturbation theory
8 Bifurcation theory I: stationary points
9 Bifurcation theory II: periodic orbits and maps
10 Bifurcational miscellany
11 Chaos
12 Global bifurcation theory
Notes and further reading
Bibliography
Index

Download File Size:15.69 MB

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