Normal Forms and Bifurcation of Planar Vector Fields

Normal Forms and Bifurcation of Planar Vector Fields

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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. The theory has developed rapidly over the past two decades. Chapters 1 and 2 of the book introduce two systematic methods of simplifying equations: centre manifold theory and normal form theory, by which the dimension of equations may be reduced and the forms changed so that they are as simple as possible. Chapters 3-5 of the book study in considerable detail the bifurcation of those one- or two-dimensional equations ...