Open AccessBook
Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields
Reads0
Chats0
TLDR
In this article, the authors introduce differential equations and dynamical systems, including hyperbolic sets, Sympolic Dynamics, and Strange Attractors, and global bifurcations.Abstract:
Contents: Introduction: Differential Equations and Dynamical Systems.- An Introduction to Chaos: Four Examples.- Local Bifurcations.- Averaging and Perturbation from a Geometric Viewpoint.- Hyperbolic Sets, Sympolic Dynamics, and Strange Attractors.- Global Bifurcations.- Local Codimension Two Bifurcations of Flows.- Appendix: Suggestions for Further Reading. Postscript Added at Second Printing. Glossary. References. Index.read more
Citations
More filters
Journal ArticleDOI
Local bifurcations and feasibility regions in differential-algebraic systems
TL;DR: This paper analyzes the generic local bifurcations including those which are directly related to the singularity, and introduces the notion of a feasibility region, which consists of all equilibrium states that can be reached quasistatically from the current operating point without loss of local stability.
Journal ArticleDOI
Topological analysis of chaotic dynamical systems
TL;DR: Topological methods have been developed for the analysis of dissipative dynamical systems that operate in the chaotic regime as discussed by the authors, which are systems for which the flow rapidly relaxes to a three-dimensional subspace of phase space.
Journal ArticleDOI
Unimolecular reactions and phase space bottlenecks
Michael Davis,Stephen K. Gray +1 more
TL;DR: In this paper, phase space bottlenecks for the unimolecular decomposition of HeI2 are discussed and a combination of the two types of bottlencks yields theoretical reaction rates which are in excellent agreement with classical numerical simulations.
Journal ArticleDOI
Static bifurcations in electric power networks: Loss of steady-state stability and voltage collapse
TL;DR: In this paper, the authors present an analysis of static stability in electric power systems based on a model consisting of the classical swing equation characterization for generators and constant admittance, PV bus and/or PQ bus load representations which leads to a semi-explicit (or constrained) system of differential equations.
Journal ArticleDOI
Oscillator death in systems of coupled neural oscillators
G. B. Ermentrout,Nancy Kopell +1 more
TL;DR: In this paper, it is shown that in the presence of large interactions, a pair or a chain of oscillators may develop a new stable equilibrium state that corresponds to the cessation of oscillation.