Local Bifurcations Center Manifolds And Normal Forms In Infinite Dimensional Dynamical Systems

Local Bifurcations, Center Manifolds, and Normal Forms in Infinite-dimensional Dynamical Systems

Local Bifurcations, Center Manifolds, and Normal Forms in Infinite-Dimensional Dynamical Systems

An extension of different lectures given by the authors, Local Bifurcations, Center Manifolds, and Normal Forms in Infinite Dimensional Dynamical Systems provides the reader with a comprehensive overview of these topics. Starting with the simplest bifurcation problems arising for ordinary differential equations in one- and two-dimensions, this book describes several tools from the theory of infinite dimensional dynamical systems, allowing the reader to treat more complicated bifurcation problems, such as bifurcations arising in partial differential equations. Attention is restricted to the study of local bifurcations with a focus upon the center manifold reduction and the normal form theory; two methods that have been widely used during the last decades. Through use of step-by-step examples and exercises, a number of possible applications are illustrated, and allow the less familiar reader to use this reduction method by checking some clear assumptions. Written by recognised experts in the field of center manifold and normal form theory this book provides a much-needed graduate level text on bifurcation theory, center manifolds and normal form theory. It will appeal to graduate students and researchers working in dynamical system theory.

Patterns of Dynamics

Theoretical advances in dynamical-systems theory and their applications to pattern-forming processes in the sciences and engineering are discussed in this volume that resulted from the conference Patterns in Dynamics held in honor of Bernold Fiedler, in Berlin, July 25-29, 2016.The contributions build and develop mathematical techniques, and use mathematical approaches for prediction and control of complex systems. The underlying mathematical theories help extract structures from experimental observations and, conversely, shed light on the formation, dynamics, and control of spatio-temporal patterns in applications. Theoretical areas covered include geometric analysis, spatial dynamics, spectral theory, traveling-wave theory, and topological data analysis; also discussed are their applications to chemotaxis, self-organization at interfaces, neuroscience, and transport processes.