Bifurcation of Singular Solutions in Reversible Systems and Applications to Reaction-Diffusion Equations.
Abstract
Dynamical systems that are reversible in the sense of Moser are investigated and bifurcation of trajectories connecting saddle points from stationary solutions is studied. As an application, reaction-diffusion models in one space dimension are considered. These equations are studied in the neighborhood of a point, where the set of spatially homogeneous solutions displays a Hopf bifurcation. It is shown that from such a point branches of solutions bifurcate, which can be described as waves travelling to or from a center. These waves may be exponentially damped at infinity or not. They can be regarded as one-dimensional analogues of 'target patterns' or 'spiral waves'. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 1981
- Accession Number
- ADA103864
Entities
People
- Michael Renardy
Organizations
- University of Wisconsin–Madison