Although, bifurcation theory of equations with autonomous and periodic time dependence is a major object of research in the study of dynamical systems since decades, the notion of a nonautonomous bifurcation is not yet established. In this book, two different approaches are developed which are based on special definitions of local attractivity and repulsivity. It is shown that these notions lead to nonautonomous Morse decompositions, which are useful to describe the global asymptotic behavior of systems on compact phase spaces. Furthermore, methods from the qualitative theory for linear and nonlinear systems are derived, and nonautonomous counterparts of the classical one-dimensional autonomous bifurcation patterns are developed.
| ISBN: | 9783540712244 |
| Publication date: | 8th June 2007 |
| Author: | Martin Rasmussen |
| Publisher: | Springer an imprint of Springer Berlin Heidelberg |
| Format: | Paperback |
| Pagination: | 217 pages |
| Series: | Lecture Notes in Mathematics |
| Genres: |
Differential calculus and equations Cybernetics and systems theory |
Although, bifurcation theory of equations with autonomous and periodic time dependence is a major object of research in the study of dynamical systems since decades, the notion of a nonautonomous bifurcation is not yet established. In this book, two different approaches are developed which are based on special definitions of local attractivity and repulsivity. It is shown that these notions lead to nonautonomous Morse decompositions, which are useful to describe the global asymptotic behavior of systems on compact phase spaces. Furthermore, methods from the qualitative theory for linear and nonlinear systems are derived, and nonautonomous counterparts of the classical one-dimensional autonomous bifurcation patterns are developed.
Attractivity and Bifurcation for Nonautonomous Dynamical Systems features in the following genres: Differential calculus and equations, Cybernetics and systems theory
Attractivity and Bifurcation for Nonautonomous Dynamical Systems is available in Paperback
Attractivity and Bifurcation for Nonautonomous Dynamical Systems was written by Martin Rasmussen and published by Springer an imprint of Springer Berlin Heidelberg
Attractivity and Bifurcation for Nonautonomous Dynamical Systems has 217 pages
Yes it is part of Lecture Notes in Mathematics series