Bifurcation theory of functional differential equations / Shangjiang Guo, Jianhong Wu

Among the recent textbooks on functional differential equations (FDEs) and delay differential equations (DDEs), this book is unique by its focus on the fundamental mathematical aspects of bifurcation theory. Following this approach, it starts with an introductory overview over classical results on codimension-one and codimension-two bifurcations for ordinary differential equations. Then DDEs and neutral FDEs are introduced as infinite dimensional dynamical systems. The authors follow here mainly the approach presented in the classical textbook by Hale and Verduyn Lunel. As the basic mathematical tools for the study of bifurcations, the authors introduce the method of center manifold reduction, normal forms, and Lyapunov-Schmidt reduction, indicating in particular, how these objects can be calculated in various cases.

The second part of the book is devoted to more specific topics, giving an exposition of degree thery for FDEs and bifurcations in systems with symmetry. Again after recalling the basic concepts from the ODE case, the authors give an introduction how they can be adapted do FDEs.

The book contains a series of illustrating figures and examples to elaborate the presented theoretical concepts. It is written in a self-contained manner, however for a reader it might be helpful to have some background in classical dynamical systems and finite dimensional bifurcation theory. The book contains a comprehensive list of references to the subject and can be particularly helpful for readers who are interested in the mathematical details that arise in the study of bifurcations in functional differential equations. (Zentralblatt)

Bibliogr. p. 275-286. Index