Normal Forms and Bifurcation of Planar Vector Fields

This book is mainly concerned with the bifurcation theory of ODEs. Chapters 1 and 2 of the book introduce two systematic methods of simplifying equations: center manifold theory and normal form theory, by which one may reduce the dimension of equations and change forms of equations to be as simple as possible. Chapters 3-5 of the book study in considerable detail the bifurcation of those one or two dimensional equations with one, two or several parameters.

This book is concerned with the bifurcation theory, the study of the changes in the structures of the solution of ordinary differential equations as parameters of the model vary.